M. Abramowitz and I. A. Stegun, Handbook of mathematical functions : with formulas, graphs, and mathematical tables, 1970.

A. Adriani, F. Cairo, L. Pulvirenti, F. Cardillo, M. Viterbini et al., Stratospheric background aerosol and polar cloud observations by laser backscattersonde within the framework of the European project "Stratospheric Regular Sounding", Annales Geophysicae, vol.17, issue.10, pp.1352-1360, 1999.
DOI : 10.1007/s00585-999-1352-2

URL : https://hal.archives-ouvertes.fr/hal-00329141

H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol.19, 1974.

C. Ammann and P. Naveau, Statistical analysis of tropical explosive volcanism occurrences over the last 6 centuries, Geophysical Research Letters, vol.102, issue.5, pp.10-1029, 2003.
DOI : 10.1029/2002GL016388

C. Ammann, G. A. Meehl, W. Washington, and C. Zender, A monthly and latitudinally varying volcanic forcing dataset in simulations of 20th century climate, Geophysical Research Letters, vol.16, issue.D23, pp.10-1029, 2003.
DOI : 10.1029/2003GL016875

C. Ammann, F. Joos, D. Schimel, B. Otto-bliesner, and R. Tomas, Solar influence on climate during the past millennium: Results from transient simulations with the NCAR Climate System Model, Proc. Nat. Acad. Science, pp.3713-3718, 2007.
DOI : 10.1073/pnas.0605064103

M. Basseville and I. V. Nikiforov, Detection of abrupt changes : Theory and Application, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00008518

M. Basseville and I. V. Nikiforov, Detection of abrupt changes : Theory and Application, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00008518

C. Beaulieu, T. B. Ouarda, and O. Seidou, Synth??se des techniques d'homog??n??isation des s??ries climatiques et analyse d'applicabilit?? aux s??ries de pr??cipitations, Hydrological Sciences Journal, vol.12, issue.1, pp.18-37, 2007.
DOI : 10.1175/1520-0442(1996)009<3548:DDITSO>2.0.CO;2

W. Bell, Signal extraction for nonstationary time series. The Annals of Statistics, pp.646-664, 1984.

S. Berthier, P. Chazette, J. Pelon, and B. Baum, Comparison of cloud statistics from spaceborne lidar systems, Atmospheric Chemistry and Physics Discussions, vol.8, issue.2, pp.5269-5304, 2008.
DOI : 10.5194/acpd-8-5269-2008

URL : https://hal.archives-ouvertes.fr/hal-00344427

C. M. Bishop, Information Theory, Inference, and Learning Algorithms, 2006.

K. F. Boersma, H. J. Eskes, E. W. Meijer, and H. M. Kelder, Estimates of lightning NO<sub>x</sub> production from GOME satellite observations, Atmospheric Chemistry and Physics Discussions, vol.5, issue.3, pp.3047-3104, 2005.
DOI : 10.5194/acpd-5-3047-2005

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles, J. Wiley and Sons, 1983.
DOI : 10.1002/9783527618156

J. Boreux, P. Naveau, O. Guin, L. Perreault, and J. Bernier, Extracting a common high frequency signal from northern quebec black spruce tree-rings with a bayesian hierarchical model, Climate of the Past, vol.55194, issue.4, pp.607-613, 2009.

R. Bourbonnais and M. Terraza, Analyse des séries temporelles, 2004.

R. Bradley, The explosive volcanic eruption signal in northern hemisphere continental temperature records, Climatic Change, vol.53, issue.C2, pp.221-243, 1988.
DOI : 10.1007/BF00139431

K. Briffa, P. Jones, F. Schweingruber, and T. Osborn, Influence of volcanic eruptions on Northern Hemisphere summer temperature over the past 600 years, Nature, vol.393, issue.6684, pp.450-455, 1998.
DOI : 10.1038/30943

P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting, 2002.

E. Castellano, S. Becagli, J. Jouzel, A. Migliori, M. Severi et al., Volcanic eruption frequency over the last 45 ky as recorded in Epica-Dome C ice core (East Antarctica) and its relationship with climatic changes, Global and Planetary Change, vol.42, issue.1-4, pp.195-205, 2004.
DOI : 10.1016/j.gloplacha.2003.11.007

H. Caussinus and O. Mestre, Detection and correction of artificial shifts in climate series, Journal of the Royal Statistical Society: Series C (Applied Statistics), vol.6, issue.3, pp.405-425, 2004.
DOI : 10.1029/2001GL014619

S. I. Chang and K. Zhang, Statistical Process Control for Variance Shift Detections of Multivariate Autocorrelated Processes, Quality Technology & Quantitative Management, vol.4, issue.3, pp.413-435, 2007.
DOI : 10.1080/16843703.2007.11673161

P. Chazette, C. David, L. J. , G. S. , and M. G. , Comparative lidar study of the optical, geometrical, and dynamical properties of stratospheric post-volcanic aerosols, following the eruptions of El Chichon and Mount Pinatubo, Journal of Geophysical Research, vol.21, issue.5, pp.195-207, 1995.
DOI : 10.1029/95JD02268

P. Chazette, J. Pelon, and G. Megie, Determination by spaceborne backscatter lidar of the structural parameters of atmospheric scattering layers, Applied Optics, vol.40, issue.21, pp.3428-3440, 2001.
DOI : 10.1364/AO.40.003428

S. Chib, Estimation and comparison of multiple change-point models, Journal of Econometrics, vol.86, issue.2, pp.221-241, 1998.
DOI : 10.1016/S0304-4076(97)00115-2

L. , C. Sloan, and D. Pollard, Polar stratospheric clouds : A high latitude warming mechanism in an ancient greenhouse world, Geophysical Research Letters, vol.25, 1998.

H. Clausen, C. Hammer, C. Hvidberg, D. Dahl-jensen, J. Steffensen et al., A comparison of the volcanic records over the past 4000 years from the Greenland Ice Core Project and Dye 3 Greenland ice cores, Journal of Geophysical Research: Oceans, vol.264, issue.D8, 1997.
DOI : 10.1029/97JC00587

R. Collis and P. Russell, Lidar measurement of particles and gases by elastic backscattering and differential absorption, laser monitoring of the atmosphere, Applied Physics : Laser Monitoring of the Atmosphere, vol.14, 1976.

T. Crowley, Causes of Climate Change Over the Past 1000 Years, Science, vol.289, issue.5477, pp.270-277, 2000.
DOI : 10.1126/science.289.5477.270

T. J. Crowley and K. Kim, Modeling the temperature response to forced climate change over the last six centuries, Geophysical Research Letters, vol.14, issue.13, 1999.
DOI : 10.1029/1999GL900347

R. Dalang and D. Conus, Introduction à la théorie des probabilités, 2008.

C. David, Etude des nuages stratosphériques polaires et des aérosols volcaniques en régions polaires par sondage laser, 1995.

B. C. David, S. Bekki, S. Godin, G. Mégie, and M. P. Chipperfield, Polar stratospheric clouds climatology over Dumont d'Urville between 1989 and 1993 and the influence of volcanic aerosols on their formation, Journal of Geophysical Research: Atmospheres, vol.259, issue.23, pp.163-180, 1998.
DOI : 10.1029/98JD01692

C. David, S. Bekki, N. Berdunov, M. Marchand, M. Snels et al., Classification and scales of Antarctic polar stratospheric clouds using wavelet decomposition, Journal of Atmospheric and Solar-Terrestrial Physics, vol.67, issue.3, pp.293-300, 2004.
DOI : 10.1016/j.jastp.2004.07.043

URL : https://hal.archives-ouvertes.fr/hal-00074920

C. David, P. Keckhut, A. Armetta, J. Jumelet, M. Marchand et al., Radiosondes stratospheric temperatures from 1957 to 2008 at Dumont d'Urville (Antarctica): trends and link with Polar Stratospheric Clouds, Atmospheric Chemistry and Physics Discussions, vol.9, issue.6, pp.25687-25722, 2009.
DOI : 10.5194/acpd-9-25687-2009

R. A. Davis, T. C. Lee, and G. A. Rodriguez-yam, Structural break estimation for nonstationary time series signals, J.American Statist. Assoc, vol.101, pp.229-239, 2006.
DOI : 10.1198/016214505000000745

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

D. Montera, Etude de la variabilité micro-échelle des précipitations : Application à la propagation des ondes millimétriques en SATCOM, 2008.

R. Delmas, G. Mégie, and V. Peuch, Physique et chimie de l'atmosphère, 2005.

A. Dempster, N. Laird, D. B. Rubin, L. Sloan, and D. Pollard, Maximum likelihood from incomplete data via the em algorithm, Journal of the Royal Statistical Society, vol.39, 1977.

J. Diard, P. Bessiere, and E. Mazer, A Survey of Probabilistic Models Using the Bayesian Programming Methodology as a Unifying Framework, International Conference on Computational Intelligence, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00019254

A. Doucet, N. D. Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice, 2001.
DOI : 10.1007/978-1-4757-3437-9

J. Droesbeke, M. Lejeune, and G. Saporta, Méthodes statistique pour données qualitatives, 2005.

A. Dubietis, P. Dalin, R. Balciunas, and K. Cernis, Observations of noctilucent clouds from Lithuania, Journal of Atmospheric and Solar-Terrestrial Physics, vol.72, issue.14-15, pp.14-151090, 2010.
DOI : 10.1016/j.jastp.2010.07.004

H. Egon and P. Porée, Statistique et probabilités en production industrielle Contrôle et maîtrise de la qualité, fiabilité, problèmes et exercices corrigés. Hermann, éditeurs des sciences et des arts, 2003.

A. Einstein, ??ber die von der molekularkinetischen Theorie der W??rme geforderte Bewegung von in ruhenden Fl??ssigkeiten suspendierten Teilchen, Annalen der Physik, vol.11, issue.8, pp.549-560, 1905.
DOI : 10.1002/andp.19053220806

G. Evensen, The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynamics, vol.53, issue.4, 2003.
DOI : 10.1007/s10236-003-0036-9

G. Evensen, Data Assimilation : The Ensemble Kalman Filter, 2006.
DOI : 10.1007/978-3-642-03711-5

G. Evensen, Data Assimilation : The Ensemble Kalman Filter, 2009.
DOI : 10.1007/978-3-642-03711-5

F. Fernald, B. Herman, and J. Reagan, Determination of Aerosol Height Distributions by Lidar, Journal of Applied Meteorology, vol.11, issue.3, p.482, 1972.
DOI : 10.1175/1520-0450(1972)011<0482:DOAHDB>2.0.CO;2

F. Fierli, A. Hauchecorne, and B. Knudsen, Analysis of polar stratospheric clouds using temperature and aerosols measured by the Alomar R/M/R lidar, Journal of Geophysical Research: Atmospheres, vol.1997, issue.D20, p.127, 2001.
DOI : 10.1029/2001JD900062

G. Fiocco and L. Smullins, Detection of Scattering Layers in the Upper Atmosphere (60???140 km) by Optical Radar, Nature, vol.194, issue.4900, p.1275, 1963.
DOI : 10.1103/PhysRevLett.10.89

B. Fontaine and S. Louvet, Sudan-Sahel rainfallonset : Definition of an objective index, types of years, and experimental hindcasts, J. Geophys. Res, p.111, 2006.

B. Fontaine, S. Louvet, and P. Roucou, Definition and predictability of an OLR-based West African monsoon onset, International Journal of Climatology, vol.5, issue.3, pp.1787-1798, 2008.
DOI : 10.1002/joc.1674

URL : https://hal.archives-ouvertes.fr/hal-00320782

A. Fraser, F. Goutail, C. A. Mclinden, S. M. Melo, and K. Strong, Lightning-produced NO2 observed by two ground-based UV-visible spectrometers at Vanscoy, Saskatchewan in, Atmospheric Chemistry and Physics, vol.7, issue.6, p.1692, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00328492

S. Frontier, D. Davoult, V. Gentilhomme, and Y. Lagadeux, Statistique pour les sciences de la vie et de l'environnement, 2007.

C. Gao, A. Robock, S. Self, J. B. Witter, J. Steffenson et al., The 1452 or 1453 A.D. Kuwae eruption signal derived from multiple ice core records: Greatest volcanic sulfate event of the past 700 years, Journal of Geophysical Research, vol.102, issue.D9, pp.111-121, 1029.
DOI : 10.1029/2005JD006710

C. Gao, L. Oman, A. Robock, and G. Stenchikov, Atmospheric volcanic loading derived from bipolar ice cores: Accounting for the spatial distribution of volcanic deposition, Journal of Geophysical Research, vol.100, issue.D1
DOI : 10.1029/2006JD007461

C. Gao, A. Robock, and C. Ammann, Volcanic forcing of climate over the past 1500 years : An improved ice-core based index for climate models, Journal of Geophysical Research, 2008.

J. Gazeaux, D. Batista, C. Ammann, P. Naveau, C. Jégat et al., Extracting common pulse-like signals from multiple ice core time series, Computational Statistics & Data Analysis, vol.58, 2009.
DOI : 10.1016/j.csda.2012.01.024

URL : https://hal.archives-ouvertes.fr/hal-00922271

B. Goldfarb and C. Pardoux, Introduction à la méthode statistique, 2007.

S. Gosset and W. , The probable error of a mean, Biometrika, pp.1-25, 1908.

F. N. Gumedze, S. J. Welham, B. J. Gogel, and R. Thompson, A variance shift model for detection of outliers in the linear mixed model, Computational Statistics & Data Analysis, vol.54, issue.9, pp.2128-2144, 2010.
DOI : 10.1016/j.csda.2010.03.019

W. Guo, Y. Wang, and M. B. Brown, A Signal Extraction Approach to Modeling Hormone Time Series with Pulses and a Changing Baseline, Journal of the American Statistical Association, vol.39, issue.3, pp.746-756, 1998.
DOI : 10.1007/BF00934498

W. Guo, Y. Wang, and M. Brown, A Signal Extraction Approach to Modeling Hormone Time Series with Pulses and a Changing Baseline, Journal of the American Statistical Association, vol.39, issue.3, pp.746-756, 1999.
DOI : 10.1007/BF00934498

Y. Guo and Y. Ding, Long-Term Free-Atmosphere Temperature Trends in China Derived from Homogenized In Situ Radiosonde Temperature Series, Journal of Climate, vol.22, issue.4, pp.1037-1051, 2001.
DOI : 10.1175/2008JCLI2480.1

S. Hagos and K. Cook, Dynamics of the West African Monsoon Jump, Journal of Climate, vol.20, issue.21, pp.5264-5284, 2007.
DOI : 10.1175/2007JCLI1533.1

T. M. Hamill and C. Snyder, A Hybrid Ensemble Kalman Filter???3D Variational Analysis Scheme, Monthly Weather Review, vol.128, issue.8, 2000.
DOI : 10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2

C. Hammer, Past volcanism revealed by Greenland Ice Sheet impurities, Nature, vol.15, issue.5637, pp.482-486, 1977.
DOI : 10.1038/270482a0

A. Hannart and P. Naveau, Bayesian multiple change points and segmentation: Application to homogenization of climatic series, Water Resources Research, vol.10, issue.4, pp.10-1029, 2009.
DOI : 10.1029/2008WR007689

J. Hansen and C. , Climate forcings in Goddard Institute for Space Studies SI2000 simulations, Journal of Geophysical Research, vol.351, issue.D18, 2002.
DOI : 10.1029/2001JD001143

G. Hegerl, T. Crowley, S. Baum, K. Kim, and W. Hyde, Detection of volcanic, solar and greenhouse gas signals in paleo-reconstructions of nothern hemispheric temperature

G. Hegerl, T. Crowley, W. Hyde, and D. Frame, Climate sensitivity constrained by temperature reconstructions over the past seven centuries, Nature, vol.13, issue.7087, pp.1029-1032, 2006.
DOI : 10.1038/nature04679

G. C. Hegerl, F. W. Zwiers, P. Braconnot, N. P. Gillett, Y. Luo et al., 9 supplementary materials understanding and attributing climate change coordinating lead authors, Contribution of Working Group I to the fourth assessment report of the Intergovernmental Panel on climate change, 2007.

I. B. Hossack, J. H. Pollard, and B. Zehnwirth, Introductory statistics with applications in general insurance, 1999.
DOI : 10.1017/CBO9781139173322

M. K. Hughes and C. M. Ammann, The future of the past???an earth system framework for high resolution paleoclimatology: editorial essay, Climatic Change, vol.47, issue.4, 2009.
DOI : 10.1007/s10584-009-9588-0

S. Janicot, C. D. Thorncroft, and A. , Large-scale overview of the summer monsoon over West Africa during the AMMA field experiment in 2006, Annales Geophysicae, vol.26, issue.9, pp.2569-2595, 2006.
DOI : 10.5194/angeo-26-2569-2008

URL : https://hal.archives-ouvertes.fr/insu-00388742

P. Jones, A. Moberg, T. Osborn, and K. Briffa, Surface climate responses to explosive volcanic eruptions seen in long European temperature records and mid-to-high latitude tree-ring density around the Northern Hemisphere, Geophysical monograph, vol.100, issue.4, pp.239-254, 2003.
DOI : 10.1029/139GM15

C. E. Junge, C. W. Chagnon, and J. E. Manson, A World-wide Stratospheric Aerosol Layer, Science, vol.133, issue.3463, pp.1478-1479, 1961.
DOI : 10.1126/science.133.3463.1478-a

R. E. 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

R. E. Kalman and R. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-107, 1961.
DOI : 10.1115/1.3658902

M. Kanamitsu, W. Ebisuzaki, J. Woollen, S. Yang, J. Hnilo et al., Bulletin of the, pp.1631-1643, 2002.

R. W. Katz, Sir Gilbert Walker and a Connection between El Ni??o and Statistics, Statistical Science, vol.17, issue.1, 2002.
DOI : 10.1214/ss/1023799000

R. Keen, Volcanic aerosol optical thicknesses since 1960, Global Volcanism Network, vol.26, 2001.

J. Klett, Stable analytical inversion solution for processing lidar returns, Applied Optics, vol.20, issue.2, 1981.
DOI : 10.1364/AO.20.000211

J. Klett, Lidar inversion with variable backscatter/extinction ratios, Applied Optics, vol.24, issue.11, p.1638, 1985.
DOI : 10.1364/AO.24.001638

R. Kohn and C. F. Ansley, Signal extraction for finite nonstationary time series, Biometrika, vol.74, issue.2, pp.411-421, 1987.
DOI : 10.1093/biomet/74.2.411

V. A. Kovalev and W. E. Eichinger, Elastic Lidar : Theory, Practice, and Analysis Methods, 2004.
DOI : 10.1002/0471643173

A. Kurbatov, G. Zielinski, N. Dunbar, P. Mayewski, S. Meyerson et al., 000 year record of explosive volcanism in the siple dome ice core, west antarctica, Journal of Geophysical Research, vol.12, issue.111, pp.10-1029, 2006.

T. Lachlan-cope, W. Connolley, J. Turner, H. Roscoe, G. Marshall et al., Antarctic winter tropospheric warming -the potential role of polar stratospheric clouds, a sensity study, Atmopsheric Sceince Letters, vol.10, 2009.

H. Lamb, Volcanic Dust in the Atmosphere; with a Chronology and Assessment of Its Meteorological Significance, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.266, issue.1178, pp.425-533, 1970.
DOI : 10.1098/rsta.1970.0010

C. J. Langway, K. Osada, H. Clausen, C. U. Hammer, and H. Shoji, A 10-century comparison of prominent bipolar volcanic events in ice cores, Journal of Geophysical Research, vol.264, issue.5, 1995.
DOI : 10.1029/95JD01175

M. Lavielle and E. Lebarbier, an application of MCMC methods for the multiple changepoints problem, Signal Process, pp.39-53, 2001.

L. , L. Barbé, T. Lebel, and D. Tapsoba, Rainfall variability in west africa during the years 1950-90, Journal of Climate, vol.152, issue.2, pp.187-202, 2002.

B. Legras, O. Mestre, E. Bard, and P. Yiou, On misleading solar-climate relationship, Climate of the Past Discussions, vol.6, issue.3, pp.767-800, 2010.
DOI : 10.5194/cpd-6-767-2010-supplement

B. Liebmann and C. Smith, Description of a complete outgoing longwave radiation dataset, Bull. Amer. Meteor. Soc, vol.77, pp.1275-1277, 1996.

N. Mahowald, C. Luo, J. Corral, and C. Zender, Interannual variability in atmospheric mineral aerosols from a 22-year model simulation and observational data, Journal of Geophysical Research, vol.10, issue.3, pp.10-1029, 2003.
DOI : 10.1029/2002JD002821

E. D. Maloney and J. Shaman, Intraseasonal Variability of the West African Monsoon and Atlantic ITCZ, Journal of Climate, vol.21, issue.12, pp.2898-2918, 2008.
DOI : 10.1175/2007JCLI1999.1

R. Mankiewicz, Histoire des mathématiques, 2001.

M. Manoliu and T. Stathis, Energy futures prices : Term structure models with kalman filter estimation. MSIS Department and Center for Computational Finance, 2002.

J. C. Maxwell, On the dynamical theory of gases, Phil. Mag, vol.32, pp.390-393, 1866.

P. Mayewski, W. Lyons, M. Spencer, M. Twickler, P. Koci et al., Sulfate and Nitrate Concentrations from a South Greenland Ice Core, Science, vol.232, issue.4753, pp.975-977, 1986.
DOI : 10.1126/science.232.4753.975

R. E. Mcculloch and R. S. Tsay, Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series, Journal of the American Statistical Association, vol.29, issue.423, pp.968-978, 1993.
DOI : 10.1002/for.3980070102

A. Mccutcheon, Latent class analysis, 1987.

R. J. Meinhold and N. D. Singpurwalla, Understanding the Kalman Filter. The American Statistician, pp.123-127, 1983.

O. Mestre and H. Caussinus, A Correction Model for Homogenisation of Long Instrumental Data Series, Detecting and modelling regional climate change, pp.13-19, 2001.
DOI : 10.1007/978-3-662-04313-4_2

J. M. Moisselin, M. Schneider, C. Canellas, and O. Mestre, Changements climatiques en france au 20ème siècle -Étude des longues séries de données homogénéisées françaises de précipitations et températures, pp.45-56, 2002.

A. M. Mood, Introduction to the Theory of, Statistics, 1974.

Y. Morille, M. Haeffelin, P. Drobinski, and J. Pelon, STRAT: An Automated Algorithm to Retrieve the Vertical Structure of the Atmosphere from Single-Channel Lidar Data, Journal of Atmospheric and Oceanic Technology, vol.24, issue.5, pp.761-775, 2007.
DOI : 10.1175/JTECH2008.1

URL : https://hal.archives-ouvertes.fr/hal-00147430

E. Mosley-thompson, L. Thompson, J. Dai, M. Davis, and P. Lin, Climate of the last 500 years: High resolution ice core records, Quaternary Science Reviews, vol.12, issue.6, 1993.
DOI : 10.1016/S0277-3791(05)80006-X

P. Naveau and C. Ammann, Statistical distributions of ice core sulfate from climatically relevant volcanic eruptions, Geophysical Research Letters, vol.264, issue.D6, pp.10-1029, 2005.
DOI : 10.1029/2004GL021732

P. Naveau, C. Ammann, H. Oh, and W. Guo, An automatic statistical methodology to extract pulse-like forcing factors in climatic time series: Application to volcanic events, Geophysical monograph, vol.264, issue.D6, pp.177-186, 2003.
DOI : 10.1029/139GM11

R. Finkel, Sulphate and nitrate concentrations in snow from South Greenland 1895-1978, Nature, vol.314, pp.611-613, 1985.

C. Newhall and S. Self, The volcanic explosivity index (VEI) an estimate of explosive magnitude for historical volcanism, Journal of Geophysical Research, vol.35, issue.C2, pp.1231-1238, 1982.
DOI : 10.1029/JC087iC02p01231

S. Nicholson, Rainfall and Atmospheric Circulation during Drought Periods and Wetter Years in West Africa, Monthly Weather Review, vol.109, issue.10, pp.2191-2208, 1981.
DOI : 10.1175/1520-0493(1981)109<2191:RAACDD>2.0.CO;2

. Ouachani and O. Bargaoui, Integration of a Kalman filter in the HBV hydrological model for runoff forecasting, 2010.

J. Palais, M. Germani, and G. Zielinski, Interhemispheric transport of volcanic ash from a 1259 ad volcanic-eruption to the greenland and antarctic ice sheets, GRL, vol.19, 1992.

T. Palmer, A. S. Van-ommen, M. A. Curran, V. Morgan, J. Souney et al., High-precision dating of volcanic events (A.D. 1301-1995) using ice cores from Law Dome, Antarctica, Journal of Geophysical Research: Atmospheres, vol.100, issue.43, 2001.
DOI : 10.1029/2001JD000330

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

T. Peter, MICROPHYSICS AND HETEROGENEOUS CHEMISTRY OF POLAR STRATOSPHERIC CLOUDS, Annual Review of Physical Chemistry, vol.48, issue.1, pp.785-822, 1997.
DOI : 10.1146/annurev.physchem.48.1.785

B. Bibliographie, C. A. Pires, O. Talagrand, and M. Bocquet, Diagnosis and impacts of non-Gaussianity of innovations in data assimilation, Physica D-Nonlinear Phenomena, vol.239, issue.17, pp.1701-1717, 2010.

C. M. Platt, Remote Sounding of High Clouds: I. Calculation of Visible and Infrared Optical Properties from Lidar and Radiometer Measurements, Journal of Applied Meteorology, vol.18, issue.9, pp.1130-11431520, 1979.
DOI : 10.1175/1520-0450(1979)018<1130:RSOHCI>2.0.CO;2

J. Puget and R. Blanchete, Le changement climatique, Académie des Sciences, 2010.

R. Development and C. Team, R : A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, 2009.

J. Reeves, J. Chen, X. L. Wang, R. Lund, and Q. Q. Lu, A Review and Comparison of Changepoint Detection Techniques for Climate Data, Journal of Applied Meteorology and Climatology, vol.46, issue.6, pp.900-915, 2007.
DOI : 10.1175/JAM2493.1

A. Ribes, Détection statistique de changement climatique, 2009.

A. Ribes, J. Azais, and S. Planton, A method for regional climate change detection using smooth temporal patterns, Climate Dynamics, vol.399, issue.3, pp.391-406, 2010.
DOI : 10.1007/s00382-009-0670-0

URL : https://hal.archives-ouvertes.fr/hal-00630201

J. Rissanen, Modeling by shortest data description, Automatica, vol.14, issue.5, pp.445-471, 1978.
DOI : 10.1016/0005-1098(78)90005-5

A. Robock, Volcanic eruptions and climate, Reviews of Geophysics, vol.23, issue.44, pp.191-219, 2000.
DOI : 10.1029/1998RG000054

A. Robock and M. Free, Ice cores as an index of global volcanism from 1850 to the present, Journal of Geophysical Research, vol.264, issue.A, pp.549-560, 1995.
DOI : 10.1029/95JD00825

A. Robock and J. Mao, The Volcanic Signal in Surface Temperature Observations, Journal of Climate, vol.8, issue.5, pp.1086-1103, 1995.
DOI : 10.1175/1520-0442(1995)008<1086:TVSIST>2.0.CO;2

J. Rosen, D. Hofmann, and J. Laby, Stratospheric Aerosol Measurements II: The Worldwide Distribution, Journal of the Atmospheric Sciences, vol.32, issue.7, pp.1457-1462, 1975.
DOI : 10.1175/1520-0469(1975)032<1457:SAMITW>2.0.CO;2

C. Saporta, Modèles à variables latentes et modèles de mélange, pp.243-284, 2008.

S. Sarkka, V. Aki, and J. Lampinen, Time series prediction by kalman smoother with cross-validated noise density, 2006.

M. Sato, J. Hansen, M. P. Mccormick, and J. Pollack, Stratospheric aerosol optical depths, 1850???1990, Journal of Geophysical Research, vol.11, issue.D12, 1993.
DOI : 10.1029/93JD02553

G. E. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, 1978.
DOI : 10.1214/aos/1176344136

N. Shepard, Partial non-Gaussian state space, Biometrika, vol.81, issue.1, pp.115-131, 1994.
DOI : 10.1093/biomet/81.1.115

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga et al., High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols 1: Theory and instrumentation, Applied Optics, vol.22, issue.23, pp.3716-3724, 1983.
DOI : 10.1364/AO.22.003716

T. Simkin and L. Siebert, Volcanoes of the World, 1994.

M. S. Wong, J. E. Nichol, and K. Ho-lee, Modeling of Aerosol Vertical Profiles Using GIS and Remote Sensing, Sensors, vol.9, issue.6, pp.4380-4389, 2009.
DOI : 10.3390/s90604380

R. C. Sprinthall, Basic Statistical Analysis, 2009.

J. Staehelin, C. Vogler, and S. Brannimann, The Long History of Ozone Measurements: Climatological Information Derived from Long Ozone Records, Twenty Years of Ozone Decline, pp.119-131, 2009.
DOI : 10.1007/978-90-481-2469-5_9

H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 2002.

R. Stothers, The great dry fog of 1783, Climatic Change, vol.21, issue.1, 1996.
DOI : 10.1007/BF00141279

R. Stothers, Major optical depth perturbations to the stratosphere from volcanic eruptions: Pyrheliometric period, 1881-1960, Journal of Geophysical Research: Atmospheres, vol.2, issue.1, 1996.
DOI : 10.1029/95JD03237

B. Sultan and S. Janicot, Abrupt shift of the ITCZ over West Africa and intra-seasonal variability, Geophysical Research Letters, vol.40, issue.20, pp.3353-3356, 2000.
DOI : 10.1029/1999GL011285

URL : https://hal.archives-ouvertes.fr/hal-00162239

B. Sultan and S. Janicot, The West African Monsoon Dynamics. Part II: The ???Preonset??? and ???Onset??? of the Summer Monsoon, Journal of Climate, vol.16, issue.21, pp.3407-3427, 2003.
DOI : 10.1175/1520-0442(2003)016<3407:TWAMDP>2.0.CO;2

URL : https://hal.archives-ouvertes.fr/hal-00155510

A. Tabazadeh, R. Turco, and M. Jacobson, A model for studying the composition and chemical effects of stratospheric aerosols, Journal of Geophysical Research, vol.97, issue.D6, pp.12897-12914, 1994.
DOI : 10.1029/94JD00820

O. Talagrand, R. Shutyaev, . Lahoz, and . Wa, A posteriori validation of assimilation algorithms Data Assimilation for The Earth System, NATO Science Series IV Earth and Environmental Sciences, vol.26, pp.85-95, 2003.

R. Taton, Histoire générale des sciences : La science contemporaine -Le XXe siècle, 1995.

T. Thordarson and S. Self, Atmospheric and environmental effects of the 1783???1784 Laki eruption: A review and reassessment, Journal of Geophysical Research, vol.21, issue.21, pp.10-1029, 2003.
DOI : 10.1029/2001JD002042

C. Thorncroft and K. Hodges, African Easterly Wave Variability and Its Relationship to Atlantic Tropical Cyclone Activity, Journal of Climate, vol.14, issue.6, pp.1166-1179, 2001.
DOI : 10.1175/1520-0442(2001)014<1166:AEWVAI>2.0.CO;2

S. Tufféry, Data mining et statistique décisionnelle, 2010.

. Villien, Prévision de trajectoires 3-D en temps réel, 2006.

C. Voigt, J. Schreiner, A. Kohlmann, P. Zink, K. Mauersberger et al., Nitric Acid Trihydrate (NAT) in Polar Stratospheric Clouds, Science, vol.290, issue.5497, pp.1756-1758, 2000.
DOI : 10.1126/science.290.5497.1756

URL : https://hal.archives-ouvertes.fr/hal-00295666

G. , V. Cossart, P. Hoffmann, U. Vonzahn, P. Keckhut et al., Mid-latitude noctilucent cloud observations by lidar, Geophysical Research Letters, vol.23, issue.21, pp.2919-2922, 1996.

H. , V. Storch, and F. W. Zwiers, Statistical Analysis in Climate Research, 1999.

U. , V. Zahn, G. Von-cossart, J. Fiedler, K. H. Fricke et al., The alomar rayleigh/mie/raman lidar :objectives ,configuration and performance, Annales Geophysicae, vol.18, pp.815-833, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00329143

G. Wahba, Improper priors, spline smoothing and the problem of guarding against model errors in regression, J. of the Royal Stat. Soc, vol.40, p.364, 1978.

S. Wastegard and S. M. Davies, An overview of distal tephrochronology in northern Europe during the last 1000 years, Journal of Quaternary Science, vol.264, issue.3, pp.500-512, 2009.
DOI : doi: 10.1029/2002JD002449

W. E. Wecker and C. F. Ansley, The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing, Journal of the American Statistical Association, vol.30, issue.381, pp.81-89, 1983.
DOI : 10.1080/01621459.1983.10477935

G. Welch and G. Bishop, An introduction to the Kalman Filter, 1995.

G. Welch and G. Bishop, An introduction to the Kalman Filter, 2006.

T. M. Wigley, C. Ammann, B. D. Santer, and S. Raper, Effect of climate sensitivity on the response to volcanic forcing, Journal of Geophysical Research, vol.293, issue.D18, pp.10-1029, 2005.
DOI : 10.1029/2004JD005557

. Wmo, Scientific assessment of ozone depletion :2006, global ozone research and monitoring project, 2007.

J. Woods, Two-dimensional kalman filtering In Two-Dimensional Digital Signal Processing I, pp.155-205, 1981.

G. Zielinski, Use of paleo-records in determining variability within the volcanism???climate system, Quaternary Science Reviews, vol.19, issue.1-5, pp.417-438, 2000.
DOI : 10.1016/S0277-3791(99)00073-6

G. Zielinski, P. Mayewski, L. Meeker, S. Whitlow, M. Twickler et al., Record of Volcanism Since 7000 B.C. from the GISP2 Greenland Ice Core and Implications for the Volcano-Climate System, Science, vol.264, issue.5161, pp.948-952, 1994.
DOI : 10.1126/science.264.5161.948

F. Zwiers and H. V. Storch, On the role of statistics in climate research, International Journal of Climatology, vol.24, issue.6, pp.665-680, 2004.
DOI : 10.1002/joc.1027

. La-dernière-Égalité-est-appelée-formule-de-bayes, De cette définition, il découle les premiers moments conditionnels, que sont l'espérance et la variance conditionnelles définies par

E. Pour-toute-sous-tribu-a-?-f,-l-'espérance-conditionnelle, suit les propriétés suivantes : i) si X est intégrable, E[X|A] l'est aussi De même, si X ? 0, alors E[X|A] ? 0 ii) E[·|A] est linéaire, c'est à dire que ?(a, b) ? R, X et Y deux variables aléatoires réelles : E[aX + bY |A] = aE[X|A] + bE[Y |A] iii) orthogonalité : Y ? E[X|Y ] est orthogonal à X iv)

. La-variance-conditionnelle,-quant-À-elle, suit les propriétés suivantes : vi) Var, X|Y) 2 |Y ] vii) Var[X|Y ] = E[X 2 |Y ] ? (E[X|Y ]) 2

. Dans-cette-thèse, ces relations sont toutes utilisées dans les développements des algorithmes utilisant le filtre de Kalman. Il est possible d'en trouver des démonstrations dans des ouvrages de tels que [Dalang and Conus, 2008.