]. L. Amodei and . Amodei, Solution approchée pour un problème d'assimilation de données météorologiques avec prise en compte de l'erreur de modèle, Comptes rendus de l'Académie des sciences. Série 2. Sciences de la terre et des planètes, pp.3211087-1094, 1995.

]. J. Anderson, An Ensemble Adjustment Kalman Filter for Data Assimilation, Monthly Weather Review, vol.129, issue.12, pp.2884-2903, 2001.
DOI : 10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.9952

]. J. Anderson, An adaptive covariance inflation error correction algorithm for ensemble filters, Tellus A: Dynamic Meteorology and Oceanography, vol.131, issue.130, pp.210-224, 2007.
DOI : 10.1111/j.1600-0870.2006.00216.x

A. Et-anderson, ]. J. Anderson, and S. L. Anderson, A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts, Monthly Weather Review, vol.127, issue.12, pp.2741-2758, 1999.
DOI : 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2

. Andersson, The ECMWF implementation of three-dimensional variational assimilation (3D-Var). III: Experimental results, Quarterly Journal of the Royal Meteorological Society, vol.117, issue.550, pp.1241831-1860, 1998.
DOI : 10.1002/qj.49712455004

]. E. Arnaud, Méthodes de filtrage pour du suivi dans des séquences d'images ? Application au suivi de points caractéristiques, Thèse de doctorat, 2004.

]. R. Arthern, Optimal estimation of changes in the mass of ice sheets, Journal of Geophysical Research: Earth Surface, vol.246, issue.4937, 2003.
DOI : 10.1029/2003JF000021

A. Et-gudmundsson, ]. R. Arthern, and G. H. Gudmundsson, Initialization of ice-sheet forecasts viewed as an inverse Robin problem, Journal of Glaciology, issue.197, pp.56527-533, 2010.

A. Et-hindmarsh, ]. R. Arthern, and R. C. Hindmarsh, Determining the contribution of Antarctica to sea-level rise using data assimilation methods, Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences, pp.3641841-1865, 1844.

. Blayo, Assimilation variationnelle de données en océanographie et réduction de la dimension de l'espace de contrôle, Équations aux dérivées partielles et applications. Articles dédiés à Jacques-Louis Lions. Gauthier-Villars, pp.199-219, 1998.

N. Blayo, Introduction à l'assimilation de données variationnelle. Notes de cours, M2 Mathématiques, Informatique, 2012.

]. M. Bocquet, Ensemble Kalman filtering without the intrinsic need for inflation, Nonlinear Processes in Geophysics, vol.18, issue.5, pp.735-750, 2011.
DOI : 10.5194/npg-18-735-2011
URL : https://hal.archives-ouvertes.fr/hal-00646682

]. M. Bocquet and P. Sakov, Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlinear Processes in Geophysics, vol.19, issue.3, pp.383-399, 2012.
DOI : 10.5194/npg-19-383-2012
URL : https://hal.archives-ouvertes.fr/hal-00714384

. Bonan, Data assimilation in glaciology, Advanced Data Assimilation for Geosciences, 2012.
DOI : 10.1093/acprof:oso/9780198723844.003.0025
URL : https://hal.archives-ouvertes.fr/hal-00715832

. Bonan, An ETKF approach for initial state and parameter estimation in ice sheet modelling, Nonlinear Processes in Geophysics, 2013.
DOI : 10.5194/npg-21-569-2014
URL : https://hal.archives-ouvertes.fr/hal-01066882

]. F. Bouttier-et-courtier, P. Bouttier, and . Courtier, Data assimilation, concepts and methods, 1999.

]. G. Böðvarsson, On the flow of ice-sheets and glaciers, Jökull, vol.5, pp.1-8, 1955.

. Box, ]. G. Cox, D. R. Box, and . Cox, An analysis of transformations, Journal of the Royal Statistical Society. Series B (Methodological), pp.211-252, 1964.

. Brankart, Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals, Monthly Weather Review, vol.138, issue.3, pp.932-950, 2010.
DOI : 10.1175/2009MWR3085.1
URL : https://hal.archives-ouvertes.fr/hal-00491337

]. G. Broquet, Caractérisation des erreurs de modélisation pour l'assimilation de données, 2007.

]. E. Bueler-et-brown, J. Bueler, and . Brown, Shallow shelf approximation as a " sliding law " in a thermomechanically coupled ice sheet model, Journal of Geophysical Research : Earth Surface, issue.F3, p.114, 2009.

. Burgers, Analysis Scheme in the Ensemble Kalman Filter, Monthly Weather Review, vol.126, issue.6, pp.1719-1724, 1998.
DOI : 10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2

C. Et-jaoua, ]. S. Chaabane, and M. Jaoua, Identification of Robin coefficients by the means of boundary measurements, Inverse Problems, vol.15, pp.1425-170, 1999.

. Chorin, Implicit particle filters for data assimilation. arXiv preprint, 2010.
DOI : 10.2140/camcos.2010.5.221
URL : http://arxiv.org/abs/1005.4002

]. S. Cohn-et-todling, R. Cohn, and . Todling, Approximate Data Assimilation Schemes for Stable and Unstable Dynamics, Journal of the Meteorological Society of Japan. Ser. II, vol.74, issue.1, pp.63-75, 1996.
DOI : 10.2151/jmsj1965.74.1_63

. Corazza, Use of the breeding technique to estimate the structure of the analysis "errors of the day", Nonlinear Processes in Geophysics, pp.233-243, 2003.
DOI : 10.5194/npg-10-233-2003
URL : https://hal.archives-ouvertes.fr/hal-00302201

. Cornford, Adaptive mesh, finite volume modeling of marine ice sheets, Journal of Computational Physics, vol.232, issue.1, pp.529-549, 2013.
DOI : 10.1016/j.jcp.2012.08.037

. Courtier, A strategy for operational implementation of 4D-Var, using an incremental approach, Quarterly Journal of the Royal Meteorological Society, vol.45, issue.519, pp.1367-1387, 1994.
DOI : 10.1002/qj.49712051912

[. Silva, Assessing the effects of data selection in DAO's Physical-space Statistical Analysis System, Proceedings of the second international WMO symposium on assimilation of observations in meteorology and oceanography, pp.13-17, 1995.

]. D. Dee, On-line Estimation of Error Covariance Parameters for Atmospheric Data Assimilation, Monthly Weather Review, vol.123, issue.4, pp.1128-1145, 1995.
DOI : 10.1175/1520-0493(1995)123<1128:OLEOEC>2.0.CO;2

]. G. Desroziers, Mise en oeuvre, diagnostic et optimisation des schémas d'assimilation de données. Habilitation à diriger des recherches, 2007.

. Desroziers, Diagnosis of observation, background and analysis-error statistics in observation space, Quarterly Journal of the Royal Meteorological Society, vol.75, issue.613, pp.1313385-3396, 2005.
DOI : 10.1256/qj.05.108

[. Lorenzo, Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system, Ocean Modelling, vol.16, issue.3-4, pp.160-187, 2007.
DOI : 10.1016/j.ocemod.2006.08.002

. Doucet, On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, vol.10, issue.3, pp.197-208, 2000.
DOI : 10.1023/A:1008935410038

D. Et-goosse, ]. S. Dubinkina, and H. Goosse, An assessment of particle filtering methods and nudging for climate state reconstructions, Climate of the Past, vol.9, pp.1141-1152, 2013.

. Dubinkina, TESTING A PARTICLE FILTER TO RECONSTRUCT CLIMATE CHANGES OVER THE PAST CENTURIES, International Journal of Bifurcation and Chaos, vol.136, issue.12, pp.3611-3618, 2011.
DOI : 10.5194/cpd-5-2115-2009

]. S. Durbiano, Vecteurs caractéristiques de modèles océaniques pour la réduction d'ordre en assimilation de données, Thèse de doctorat, 2001.

]. P. Duval, Creep and recrystallization of polycrystalline ice, Bulletin de Minéralogie, vol.102, issue.2-3, pp.80-85, 1979.

. Ettema, Higher surface mass balance of the Greenland ice sheet revealed by high-resolution climate modeling, Geophysical Research Letters, vol.51, issue.12, p.36, 2009.
DOI : 10.1029/2009GL038110

]. G. Evensen, Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model, Journal of Geophysical Research: Oceans, vol.93, issue.C2, pp.97-17905, 1992.
DOI : 10.1029/92JC01972

]. G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, Journal of Geophysical Research, vol.109, issue.Part 4, pp.10143-10162, 1994.
DOI : 10.1029/94JC00572
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.930

A. B. Bibliographie-]-g and . Evensen, Sampling strategies and square root analysis schemes for the EnKF, Ocean Dynamics, vol.54, issue.6, pp.539-560, 2004.

]. G. Evensen, Data assimilation : the Ensemble Kalman Filter, 2007.
DOI : 10.1007/978-3-642-03711-5

]. H. Fisher, A short primer on ice cores. Lecture notes, Karthaus summer school, 2010.

. Flament, Cascading water underneath Wilkes Land, East Antarctic Ice Sheet, observed using altimetry and digital elevation models, The Cryosphere Discussions, vol.7, issue.2, pp.841-871, 2013.
DOI : 10.5194/tcd-7-841-2013
URL : https://hal.archives-ouvertes.fr/hal-01011350

F. Et-rémy, ]. T. Flament, and F. Rémy, Dynamic thinning of Antarctic glaciers from along-track repeat radar altimetry, Journal of Glaciology, vol.58, issue.211, pp.830-840, 2012.

. Fretwell, Bedmap2 : improved ice bed, surface and thickness datasets for Antarctica, pp.375-393, 2013.
DOI : 10.5194/tcd-6-4305-2012
URL : http://doi.org/10.5194/tcd-6-4305-2012

. Fujita, Nature of radio echo layering in the Antarctic Ice Sheet detected by a two-frequency experiment, Journal of Geophysical Research: Solid Earth, vol.23, issue.90, pp.10413013-13024, 1999.
DOI : 10.1029/1999JB900034

F. Et-bengtsson, ]. R. Furrer, and T. Bengtsson, Estimation of highdimensional prior and posterior covariance matrices in Kalman filter variants, Journal of Multivariate Analysis, vol.98, pp.227-255, 2007.

. Gagliardini, Capabilities and performance of Elmer/Ice, a new-generation ice sheet model, Geoscientific Model Development, vol.6, issue.4, pp.1299-1318, 2013.
DOI : 10.5194/gmd-6-1299-2013

. Gaspari, ]. G. Cohn, S. E. Gaspari, and . Cohn, Construction of correlation functions in two and three dimensions, Quarterly Journal of the Royal Meteorological Society, vol.4, issue.2, pp.723-757, 1999.
DOI : 10.1002/qj.49712555417

. Gauthier, Assimilation of Simulated Wind Lidar Data with a Kalman Filter, Monthly Weather Review, vol.121, issue.6, pp.1803-1820, 1993.
DOI : 10.1175/1520-0493(1993)121<1803:AOSWLD>2.0.CO;2

. Giering, ]. R. Kaminski, T. Giering, and . Kaminski, Recipes for adjoint code construction, ACM Transactions on Mathematical Software, vol.24, issue.4, pp.437-474, 1998.
DOI : 10.1145/293686.293695
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.7838

]. F. Gillet-chaulet, Modélisation de l'écoulement de la glace polaire anisotrope et premières applications au forage de Dôme C, Thèse de doctorat, 2006.

. Gillet-chaulet, Greenland Ice Sheet contribution to sea-level rise from a new-generation ice-sheet model. The Cryosphere, pp.1561-1576, 2012.
DOI : 10.5194/tc-6-1561-2012
URL : https://hal.archives-ouvertes.fr/hal-00762945

]. D. Goldberg, A variationally derived, depth-integrated approximation to a higher-order glaciological flow model, Journal of Glaciology, vol.57, issue.201, pp.157-170, 2011.
DOI : 10.3189/002214311795306763

]. D. Goldberg-et-heimbach, P. Goldberg, and . Heimbach, Parameter and state estimation with a time-dependant adjoint marine ice sheet model. The Cryosphere Discussion, pp.2845-2890, 2013.

. Goldberg, ]. D. Sergienko, O. V. Goldberg, and . Sergienko, Data assimilation using a hybrid ice flow model. The Cryosphere, pp.315-327, 2011.
DOI : 10.5194/tc-5-315-2011
URL : http://doi.org/10.5194/tc-5-315-2011

. Goosse, Reconstructing surface temperature changes over the past 600 years using climate model simulations with data assimilation, Journal of Geophysical Research, vol.38, issue.8, p.9108, 2010.
DOI : 10.1029/2009JD012737

. Gordon, Novel approach to nonlinear/non-Gaussian Bayesian state estimation A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks, IEE Proceedings F (Radar and Signal Processing IET. [Gottwald et Majda, pp.107-113705, 1993.

]. R. Greve, A continuum-mechanical formulation for shallow polythermal ice sheets, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.355, issue.1726, pp.355921-974, 1726.
DOI : 10.1098/rsta.1997.0050
URL : http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/34856/1/Greve_1997_PhilTransRSocLond.pdf

. Greve, ]. R. Blatter, H. Greve, and . Blatter, Dynamics of ice sheets and glaciers, 2009.
DOI : 10.1007/978-3-642-03415-2

W. Griewank, A. Griewank, and . Walther, Evaluating derivatives : principles and techniques of algorithmic differentiation, 2008.
DOI : 10.1137/1.9780898717761

]. J. Griggs-et-bamber, J. L. Griggs, and . Bamber, A new 1 km digital elevation model of Antarctica derived from combined radar and laser data?Part 2 : Validation and error estimates. The Cryosphere, pp.113-123, 2009.

. Grinsted, ]. A. Dahl-jensen, D. Grinsted, and . Dahl-jensen, A Monte Carlo-tuned model of the flow in the NorthGRIP area, Annals of Glaciology, vol.35, issue.1, pp.527-530, 2002.
DOI : 10.3189/172756402781817130

. Hamill, Distance-Dependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter, Monthly Weather Review, vol.129, issue.11, pp.2776-2790, 2001.
DOI : 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2

. Joughin, Greenland flow variability from ice-sheet-wide velocity mapping, Journal of Glaciology, vol.56, issue.197, pp.56415-430, 2010.
DOI : 10.3189/002214310792447734

J. Et-uhlmann, ]. S. Julier, and J. K. Uhlmann, New extension of the Kalman filter to nonlinear systems, AeroSense'97 International Society for Optics and Photonics, pp.182-193, 1997.

]. R. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

. Kleman, Fennoscandian palaeoglaciology reconstructed using a glacial geological inversion rrlodel, Journal of Glaciology, issue.144, pp.43283-299, 1997.
DOI : 10.1017/s0022143000003233

]. H. Kushner, Approximations to optimal nonlinear filters, IEEE Transactions on Automatic Control, vol.12, issue.5, pp.546-556, 1967.
DOI : 10.1109/TAC.1967.1098671

. Larour, Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM), Journal of Geophysical Research: Earth Surface, vol.45, issue.B8, p.1022, 2012.
DOI : 10.1029/2010GL043201

L. Et-hansen, ]. W. Lawson, and J. A. Hansen, Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth, Monthly Weather Review, issue.8, pp.1321966-1981, 2004.

[. Dimet, Une étude générale d " analyse objective variationnelle des champs météorologiques, 1980.

L. Dimet and . Blum, Assimilation de données pour les fluides géophysiques, Le Dimet et J. Blum, vol.67, pp.37-68, 2002.

[. Dimet, Second-Order Information in Data Assimilation*, Monthly Weather Review, vol.130, issue.3, pp.629-648, 2002.
DOI : 10.1175/1520-0493(2002)130<0629:SOIIDA>2.0.CO;2
URL : https://hal.archives-ouvertes.fr/hal-00787272

D. Le, ]. Et-talagrand, O. Dimet, and . Talagrand, Variational algorithms for analysis and assimilation of meteorological observations : theoretical aspects, Tellus A, vol.38, issue.2, pp.97-110, 1986.

G. Le, Large sample asymptotics for the ensemble Kalman filter, The Oxford handbook on Nonlinear Filtering, pp.598-631, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00409060

]. E. Le-meur and . Meur, Spécificité de l'isostasie en contexte glaciaire. Présentation et application d'un modèle de réponse terrestre, Thèse de doctorat, 1996.

. Leeuwenburgh, The impact of ensemble filter definition on the assimilation of temperature profiles in the tropical Pacific, Quarterly Journal of the Royal Meteorological Society, vol.130, issue.613, pp.1313291-3300, 2005.
DOI : 10.1256/qj.05.90

. Lemieux-dudon, Consistent dating for Antarctic and Greenland ice cores, Quaternary Science Reviews, vol.29, issue.1-2, p.176, 2010.
DOI : 10.1016/j.quascirev.2009.11.010
URL : https://hal.archives-ouvertes.fr/insu-00562239

A. B. Bibliographie, ]. P. Lermusiaux-et-robinson, A. R. Lermusiaux, and . Robinson, Data assimilation via error subspace statistical estimation. Part I : Theory and schemes, Monthly Weather Review, issue.7, pp.1271385-1407, 1999.

. Li, Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter, Quarterly Journal of the Royal Meteorological Society, vol.134, issue.639, pp.135523-533, 2009.
DOI : 10.1002/qj.371
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.537.2241

L. Et-navon, ]. Z. Li, and I. M. Navon, Optimality of variational data assimilation and its relationship with the Kalman filter and smoother, Quarterly Journal of the Royal Meteorological Society, issue.572, pp.127661-683, 2001.

]. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, 1968.

. Livings, Unbiased ensemble square root filters, Physica D: Nonlinear Phenomena, vol.237, issue.8, pp.1021-1028, 2008.
DOI : 10.1016/j.physd.2008.01.005

]. L. Lliboutry, Anisotropic, transversely isotropic nonlinear viscosity of rock ice and rheological parameters inferred from homogenization, International Journal of Plasticity, vol.9, issue.5, pp.619-632, 1993.
DOI : 10.1016/0749-6419(93)90023-J

. Mallat, Adaptative covariance estimation of locally stationary processes, Annals of Statistics, vol.26, issue.1, pp.1-47, 1998.
DOI : 10.1214/aos/1030563977
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.9556

. Mandel, On the convergence of the ensemble Kalman filter, Applications of Mathematics, vol.56, issue.6, pp.533-541, 2011.
DOI : 10.1007/s10492-011-0031-2

M. Et-houtekamer, ]. H. Mitchell, and P. L. Houtekamer, An adaptative ensemble Kalman filter, Monthly Weather Review, vol.128, pp.416-433, 2000.

M. Et-houtekamer, ]. H. Mitchell, and P. L. Houtekamer, Ensemble Kalman filter configurations and their performance with the Logistic Map, Monthly Weather Review, vol.137, pp.4325-4343, 2009.

]. T. Miyoshi, The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter, Monthly Weather Review, vol.139, issue.5, pp.1519-1535, 2011.
DOI : 10.1175/2010MWR3570.1

]. L. Morland, Thermomechanical balances of ice sheet flows, Geophysical & Astrophysical Fluid Dynamics, vol.24, issue.1-4, pp.1-4237, 1984.
DOI : 10.1080/03091928408248191

]. L. Morland, Unconfined Ice-Shelf Flow, Dynamics of the West Antarctic Ice Sheet, pp.99-116, 1987.
DOI : 10.1007/978-94-009-3745-1_6

. Morlighem, Spatial patterns of basal drag inferred using control methods from a full-Stokes and simpler models for Pine Island Glacier, West Antarctica, Geophysical Research Letters, vol.36, issue.2, p.37, 2010.
DOI : 10.1029/2010GL043853
URL : https://hal.archives-ouvertes.fr/hal-00751442

]. M. Morzfeld and A. J. Chorin, Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation, Nonlinear Processes in Geophysics, vol.19, issue.3, pp.365-382, 2012.
DOI : 10.5194/npg-19-365-2012
URL : http://arxiv.org/abs/1109.3664

]. S. Nakano-et-ueno, G. Nakano, and . Ueno, Hybrid approach of ensemble transform and importance sampling for non-linear data assimilation, International Conference on Ensemble Methods in Geophysical Sciences, 2012.

. Nerger, A Unification of Ensemble Square Root Kalman Filters, Monthly Weather Review, vol.140, issue.7, pp.140-2335, 2012.
DOI : 10.1175/MWR-D-11-00102.1

]. E. Neveu, Application des méthodes multigrilles à l'assimilation variationnelle de données en géophysique, Thèse de doctorat, 2011.

. Ott, A local ensemble Kalman filter for atmospheric data assimilation, Tellus A: Dynamic Meteorology and Oceanography, vol.56, issue.131, pp.415-428, 2004.
DOI : 10.3402/tellusa.v56i5.14462

]. D. Paillard and F. Parrenin, The Antarctic ice sheet and the triggering of deglaciations, Earth and Planetary Science Letters, vol.227, issue.3-4, pp.263-271, 2004.
DOI : 10.1016/j.epsl.2004.08.023

]. N. Papadakis, Assimilation de données image : application au suivi de courbes et de champs de vecteurs, Thèse de doctorat, 2007.

. Papadakis, Data assimilation with the weighted ensemble Kalman filter, Tellus A: Dynamic Meteorology and Oceanography, vol.133, issue.6, pp.673-697, 2010.
DOI : 10.1080/01621459.1994.10476469
URL : https://hal.archives-ouvertes.fr/hal-00490840

P. Et-hindmarsh, ]. F. Parrenin, and R. C. Hindmarsh, Influence of a non-uniform velocity field on isochrone geometry along a steady flowline of an ice sheet, Journal of Glaciology, issue.183, pp.53612-622, 2007.

. Parrenin, Analytical solutions for the effect of topography, accumulation rate and lateral flow divergence on isochrone layer geometry, Journal of Glaciology, vol.52, issue.177, pp.52191-202, 2006.
DOI : 10.3189/172756506781828728
URL : https://hal.archives-ouvertes.fr/insu-00375735

. Parrenin, Dating the Vostok ice core by an inverse method, Journal of Geophysical Research: Atmospheres, vol.102, issue.D23, pp.31-178, 2001.
DOI : 10.1029/2001JD900245

A. B. Bibliographie and . Parrenin, New modeling of the Vostok ice flow line and implication for the glaciological chronology of the Vostok ice core, J. Siegert et J. Jouzel J. Geophys. Res, vol.109, 2004.

]. D. Parrish-et-derber, J. C. Parrish, and . Derber, The National Meteorological Center's Spectral Statistical-Interpolation Analysis System, Monthly Weather Review, vol.120, issue.8, pp.1747-1763, 1992.
DOI : 10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2

. Pattyn, Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP?HOM) The Cryosphere, pp.95-108, 2008.
DOI : 10.5194/tc-2-95-2008
URL : http://doi.org/10.5194/tc-2-95-2008

]. V. Peyaud, Rôle de la dynamique des calottes glaciaires dans les grands changements climatiques des périodes glaciaires-interglaciaires, Thèse de doctorat, 2006.

. Peyaud, Modelling the Early Weichselian Eurasian Ice Sheets: role of ice shelves and influence of ice-dammed lakes, Climate of the Past, vol.3, issue.3, pp.375-386, 2007.
DOI : 10.5194/cp-3-375-2007
URL : https://hal.archives-ouvertes.fr/hal-00330724

]. Pham, A singular evolutive interpolated Kalman filter for data assimilation in oceanography, 1996.

]. Pham, Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems, Monthly Weather Review, vol.129, issue.5, pp.1194-1207, 2001.
DOI : 10.1175/1520-0493(2001)129<1194:SMFSDA>2.0.CO;2
URL : https://hal.archives-ouvertes.fr/inria-00073082

. Pham, Filtres de Kalman singuliers évolutif pour l'assimilation de données en océnographie, C. R. Acad. Sci, vol.326, issue.4, pp.255-260, 1998.
DOI : 10.1016/s1251-8050(97)86815-2

. Pham, A singular evolutive extended Kalman filter for data assimilation in oceanography, 1996.

. Philippon, Evolution of the Antarctic ice sheet throughout the last deglaciation: A study with a new coupled climate???north and south hemisphere ice sheet model, Earth and Planetary Science Letters, vol.248, issue.3-4, pp.750-758, 2006.
DOI : 10.1016/j.epsl.2006.06.017
URL : https://hal.archives-ouvertes.fr/insu-00375738

]. D. Pollard and R. M. Deconto, A simple inverse method for the distribution of basal sliding coefficients under ice sheets, pp.953-971, 2012.

. Pritchard, Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets, Nature, vol.302, issue.7266, pp.461971-975, 2009.
DOI : 10.1038/nature08471

]. A. Quiquet, Reconstruction de la calotte polaire du Groenland au cours du dernier cycle glaciaire-interglaciaire à partir de l'association de la, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00704253

. Quiquet, Sensitivity of a Greenland ice sheet model to atmospheric forcing fields. The Cryosphere, pp.999-1018, 2012.
URL : https://hal.archives-ouvertes.fr/insu-00844054

[. Et-gudmundsson, ]. M. Raymond-pralong, and G. H. Gudmundsson, Bayesian estimation of basal conditions on Rutford Ice Stream, West Antarctica, from surface data, Journal of Glaciology, vol.57, issue.202, 2011.

. Raynaud, Objective filtering of ensemble-based background-error variances, Quarterly Journal of the Royal Meteorological Society, vol.131, issue.642, pp.1177-1199, 2009.
DOI : 10.1002/qj.438

]. S. Ricci, Assimilation variationnelle océanique : modélisation multivariée de la matrice de covariance d'erreur d'ébauche, Thèse de doctorat, 2004.

. Rignot, Ice Flow of the Antarctic Ice Sheet, Science, vol.55, issue.193, pp.3331427-1430, 2011.
DOI : 10.3189/002214309790152564

]. C. Ritz, Un modèle thermo-mécanique d'évolution pour le bassin glaciaire Antarctique Vostok-Glacier Bird : Sensibilité aux valeurs des paramètres mal connus, Thèse d'État, 1992.

. Ritz, Modeling the evolution of Antarctic ice sheet over the last 420,000 years: Implications for altitude changes in the Vostok region, Journal of Geophysical Research: Atmospheres, vol.79, issue.47, pp.10631943-31964, 2001.
DOI : 10.1029/2001JD900232

R. Et-macayeal, ]. V. Rommelaere, and D. R. , Largescale rheology of the Ross Ice Shelf, Antarctica, computed by a control method, Annals of Glaciology, vol.24, pp.43-48, 1997.

. Sacher, ]. W. Bartello, P. Sacher, and . Bartello, Sampling Errors in Ensemble Kalman Filtering. Part I: Theory, Monthly Weather Review, vol.136, issue.8, pp.3035-3049, 2008.
DOI : 10.1175/2007MWR2323.1

. Sakov, ]. P. Bertino, L. Sakov, and . Bertino, Relation between two common localisation methods for the EnKF, Computational Geosciences, vol.136, issue.2, pp.225-237, 2011.
DOI : 10.1007/s10596-010-9202-6

]. P. Sakov-et-oke, P. R. Sakov, and . Oke, A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters, Tellus A: Dynamic Meteorology and Oceanography, vol.130, issue.2, pp.361-371, 2008.
DOI : 10.1111/j.1600-0870.2007.00299.x

]. P. Sakov-et-oke, P. R. Sakov, and . Oke, Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters, Monthly Weather Review, vol.136, issue.3, pp.1042-1053, 2008.
DOI : 10.1175/2007MWR2021.1

. Sakov, An Iterative EnKF for Strongly Nonlinear Systems, Monthly Weather Review, vol.140, issue.6, pp.1988-2004, 2012.
DOI : 10.1175/MWR-D-11-00176.1

]. Y. Sasaki, A Fundamental Study of the Numerical Prediction Based on the Variational Principle, Journal of the Meteorological Society of Japan. Ser. II, vol.33, issue.6, pp.262-275, 1955.
DOI : 10.2151/jmsj1923.33.6_262

]. Y. Sasaki, An ObJective Analysis Based on the Variational Method, Journal of the Meteorological Society of Japan. Ser. II, vol.36, issue.3, pp.77-88, 1958.
DOI : 10.2151/jmsj1923.36.3_77

]. Y. Sasaki, SOME BASIC FORMALISMS IN NUMERICAL VARIATIONAL ANALYSIS, Monthly Weather Review, vol.98, issue.12, pp.98875-883, 1970.
DOI : 10.1175/1520-0493(1970)098<0875:SBFINV>2.3.CO;2

S. Et-haran, ]. T. Scambos, and T. Haran, An image-enhanced DEM of the Greenland Ice Sheet, Annals of Glaciology, vol.34, issue.1, pp.291-298, 2002.

S. Et-bertino, ]. E. Simon, and L. Bertino, Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF : a twin experiment, Ocean Science, vol.5, issue.4, pp.495-510, 2009.

]. E. Simon and L. Bertino, Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model, Journal of Marine Systems, vol.89, issue.1, pp.1-18, 2012.
DOI : 10.1016/j.jmarsys.2011.07.007

. Snyder, Obstacles to High-Dimensional Particle Filtering, Monthly Weather Review, vol.136, issue.12, pp.136-4629, 2008.
DOI : 10.1175/2008MWR2529.1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.1606

]. I. Souopgui-]-l, W. R. Tarasov, and . Peltier, Assimilation d'images pour les fluides géophysiques A geophysically constrained large ensemble analysis of the deglacial history of the North American ice-sheet complex, Thèse de doctorat, pp.359-388, 2004.

. Tippett, Ensemble Square Root Filters*, Monthly Weather Review, vol.131, issue.7, pp.1311485-1490, 2003.
DOI : 10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.332.775

. Van-de-berg, Reassessment of the antactic surface mass balance using calibrated output of a regional atmospheric climate model, Journal of Geophysical Research : Atmospheres, issue.D11, p.111, 2006.

]. P. Van-leeuwen and . Van-leeuwen, Comment on ???Data Assimilation Using an Ensemble Kalman Filter Technique???, Monthly Weather Review, vol.127, issue.6, pp.1374-1377, 1999.
DOI : 10.1175/1520-0493(1999)127<1374:CODAUA>2.0.CO;2

]. P. Van-leeuwen, A Variance-Minimizing Filter for Large-Scale Applications, Monthly Weather Review, vol.131, issue.9, pp.2071-2084, 2003.
DOI : 10.1175/1520-0493(2003)131<2071:AVFFLA>2.0.CO;2

]. P. Van-leeuwen and . Van-leeuwen, Particle Filtering in Geophysical Systems, Monthly Weather Review, vol.137, issue.12, pp.4089-4114, 2009.
DOI : 10.1175/2009MWR2835.1