A. E. Beck, P. Y. Shen, H. Beltrami, J. C. Mareschal, J. et al., A comparison of five different analyses in the interpretation of five borehole temperature data sets, Global Planet, Change, vol.6, pp.2-4, 1992.

H. Beltrami, Climate from borehole data: Energy fluxes and temperatures since 1500, Geophysical Research Letters, vol.10, issue.2, pp.211110-1029, 2002.
DOI : 10.1029/2002GL015702

V. Bense and H. Beltrami, Impact of horizontal groundwater flow and localized deforestation on the development of shallow temperature anomalies, Journal of Geophysical Research, vol.26, issue.10, pp.10-1029, 2007.
DOI : 10.1029/2006JF000703

D. D. Blackwell, J. L. Steele, and C. A. Brott, The terrain effect on terrestrial heat flow, Journal of Geophysical Research, vol.34, issue.B9, pp.4757-4772, 1980.
DOI : 10.1029/JB085iB09p04757

C. Chouinard and J. Mareschal, Selection of borehole temperature depth profiles for regional climate reconstructions, Climate of the Past, vol.3, issue.2, pp.297-313, 2007.
DOI : 10.5194/cp-3-297-2007
URL : https://hal.archives-ouvertes.fr/hal-00298170

C. Clauser, P. Giese, E. Huenges, T. Kohl, H. Lehmann et al., The thermal regime of the crystalline continental crust: Implications from the KTB, Journal of Geophysical Research: Solid Earth, vol.24, issue.2, pp.417-18441, 1997.
DOI : 10.1029/96JB03443

F. Fang, C. Pain, I. Navon, M. Piggott, G. Gorman et al., Reduced-order modelling of an adaptive mesh ocean model, International Journal for Numerical Methods in Fluids, vol.13, issue.2, pp.827-851, 2009.
DOI : 10.1002/fld.1663

A. E. Gill, Atmosphere-Ocean Dynamics, Int. Geophys. Ser, vol.30, 1982.

P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

P. J. Green, Trans-dimensional Markov chain Monte Carlo, Highly Structured Stochastic Systems, pp.179-198, 2003.

S. Gruber, L. King, T. Kohl, T. Herz, W. Haeberli et al., Interpretation of geothermal profiles perturbed by topography: the alpine permafrost boreholes at Stockhorn Plateau, Switzerland, Permafrost and Periglacial Processes, vol.55, issue.4, pp.349-357, 2004.
DOI : 10.1002/ppp.503

R. N. Harris and D. S. Chapman, Mid-latitude (30??-60?? N) climatic warming inferred by combining borehole temperatures with surface air temperatures, Geophysical Research Letters, vol.97, issue.5, pp.747-750, 2001.
DOI : 10.1029/2000GL012348

P. O. Hopcroft, K. Gallagher, and C. C. Pain, Inference of past climate from borehole temperature data using Bayesian Reversible Jump Markov chain Monte Carlo, Geophysical Journal International, vol.171, issue.3, pp.1430-1439, 2007.
DOI : 10.1111/j.1365-246X.2007.03596.x
URL : https://hal.archives-ouvertes.fr/insu-00221388

S. P. Huang, H. N. Pollack, and P. Y. Shen, Temperature trends over the past five centuries reconstructed from borehole temperatures, Nature, issue.6771, pp.403-756, 2000.

B. H. Jacobsen and V. Rath, Tuning a multiscale prior with generalized cross validation for piecewise constant paleotemperature, Geophys. Res. Abstracts, vol.9, pp.1607-7692, 2007.

K. Karhunen, Zur spektraltheorie stochastischer prozesse, Ann. Acad. Sci, vol.37, 1946.

T. Kohl, Transient thermal effects below complex topographies, Tectonophysics, vol.306, issue.3-4, pp.3-4, 1999.
DOI : 10.1016/S0040-1951(99)00063-3

T. Kohl and S. Gruber, Evidence of paleotemperature signals in mountain permafrost areas, Proceedings of the 8th International Conference on Permafrost, 2003.

T. Kohl, S. Signorelli, and L. Rybach, Three-dimensional (3-D) thermal investigation below high Alpine topography, Physics of the Earth and Planetary Interiors, vol.126, issue.3-4, pp.3-4, 2001.
DOI : 10.1016/S0031-9201(01)00255-2

D. Kosambi, Statistics in Function Space, J. Indian Math. Soc, vol.7, pp.76-88, 1943.
DOI : 10.1007/978-81-322-3676-4_15

J. Kubík, Subsurface temperature field of the Bohemian Massif, Subsurface temperature field of the Bohemian Massif, pp.110-128, 1990.
DOI : 10.1007/BF02295831

I. Kukkonen and J. , Palaeoclimate and structure: the most important factors controlling subsurface temperatures in crystalline rocks. A case history from Outokumpu, eastern Finland, Geophysical Journal International, vol.126, issue.1, pp.101-112, 1996.
DOI : 10.1111/j.1365-246X.1996.tb05270.x

A. Lachenbruch, The effect of two-dimensional topography on superficial thermal gradients, U.S. Geol. Surv. Bull, pp.1203-1204, 1969.

A. H. Lachenbruch and B. V. Marshall, Changing Climate: Geothermal Evidence from Permafrost in the Alaskan Arctic, Science, vol.234, issue.4777, pp.234-689, 1986.
DOI : 10.1126/science.234.4777.689

R. Lehoucq, D. Sorensen, and C. Yang, ARPACK Users Guide: Solution of Large-Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods, Soc. for Ind. and Appl. Math, 1998.
DOI : 10.1137/1.9780898719628

T. J. Lewis and K. Wang, Influence of terrain on bedrock temperatures , Global Planet, Change, vol.6, pp.2-4, 1992.

M. Loéve, Functions aleatoire de second ordre, Compte Rend. Acad, vol.220, 1945.

A. Malinverno, Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem, Geophysical Journal International, vol.151, issue.3, pp.675-688, 2002.
DOI : 10.1046/j.1365-246X.2002.01847.x

J. C. Mareschal and H. Beltrami, Evidence for recent warming from perturbed geothermal gradients: examples from eastern Canada, Climate Dynamics, vol.6, issue.3-4, pp.135-143, 1992.
DOI : 10.1007/BF00193525

A. Moberg, D. M. Sonechkin, K. Holmgren, N. M. Datsenko, and W. Karlén, Highly variable Northern Hemisphere temperatures reconstructed from low-and high-resolution proxy data, Nature, issue.7026, pp.433-613, 2005.

K. Mosegaard and A. Tarantola, Monte Carlo sampling of solutions to inverse problems, Journal of Geophysical Research: Solid Earth, vol.10, issue.6, pp.431-12447, 1995.
DOI : 10.1029/94JB03097

D. Nitoiu and H. Beltrami, Subsurface thermal effects of land use changes, Journal of Geophysical Research, vol.9, issue.D1, pp.100510-1029, 2005.
DOI : 10.1029/2004JF000151

J. Noetzli, S. Gruber, T. Kohl, N. Salzmann, and W. Haeberli, Three-dimensional distribution and evolution of permafrost temperatures in idealized high-mountain topography, Journal of Geophysical Research, vol.416, issue.F2, pp.2-1310, 2007.
DOI : 10.1029/2006JF000545

H. N. Pollack and S. P. Huang, Climate Reconstruction from Subsurface Temperatures, Annual Review of Earth and Planetary Sciences, vol.28, issue.1, pp.339-365, 2000.
DOI : 10.1146/annurev.earth.28.1.339

H. N. Pollack and J. E. Smerdon, Borehole climate reconstructions: Spatial structure and hemispheric averages, Journal of Geophysical Research, vol.16, issue.13, pp.10-1029, 2004.
DOI : 10.1029/2003JD004163

M. Rathinam and L. R. Petzold, A New Look at Proper Orthogonal Decomposition, SIAM Journal on Numerical Analysis, vol.41, issue.5, pp.1893-192510, 2003.
DOI : 10.1137/S0036142901389049

S. ?-afanda and J. , Effects of topography and climatic changes on the temperature in borehole GFU-1, pp.187-197, 1994.

S. ?-afanda and J. , Ground surface temperature as a function of slope angle and slope orientation and its effect on the subsurface temperature field, Tectonophysics, pp.367-37510, 1999.

S. ¸-erban, D. , S. Nielsen, and C. Demetrescu, Transylvanian heat flow in the presence of topography, paleoclimate and groundwater flow, Tectonophysics, vol.335, issue.3-4, pp.331-34410, 2001.
DOI : 10.1016/S0040-1951(01)00065-8

S. ¸-erban, D. Z. , and B. H. Jacobsen, The use of broad-band prior covariance for inverse palaeoclimate estimation, Geophys, J. Int, vol.147, issue.1, pp.29-40, 2001.

P. Y. Shen and A. E. Beck, Paleoclimate change and heat flow density inferred from temperature data in the Superior Province of the Canadian Shield, Global Planet, Change, vol.6, pp.2-4, 1992.

P. Y. Shen, H. N. Pollack, S. Huang, and K. Wang, Effects of subsurface heterogeneity on the inference of climate change from borehole temperature data: Model studies and field examples from Canada, Journal of Geophysical Research: Solid Earth, vol.98, issue.B4, pp.6383-6396, 1995.
DOI : 10.1029/94JB03136

L. Sirovich, Turbulence and the dynamics of coherent structures. II. Symmetries and transformations, Quarterly of Applied Mathematics, vol.45, issue.3, pp.573-582, 1987.
DOI : 10.1090/qam/910463

L. Sirovich, Turbulence and the dynamics of coherent structures. III. Dynamics and scaling, Quarterly of Applied Mathematics, vol.45, issue.3, pp.583-590, 1987.
DOI : 10.1090/qam/910464

L. Sirovich and M. Kirby, Low-dimensional procedure for the characterization of human faces, Journal of the Optical Society of America A, vol.4, issue.3, pp.519-524, 1987.
DOI : 10.1364/JOSAA.4.000519

D. S. Sivia and J. Skilling, Data Analysis: A Bayesian Tutorial, 2006.

M. Stieglitz and J. E. Smerdon, Characterizing Land???Atmosphere Coupling and the Implications for Subsurface Thermodynamics, Journal of Climate, vol.20, issue.1, pp.21-3710, 2007.
DOI : 10.1175/JCLI3982.1

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Wstimation, Soc. for Ind. and Appl. Math, 2005.

Z. Wang, I. Navon, F. L. Dimet, and X. Zou, The 2nd-order adjoint analysis?Theory and applications, Meteorol. Atmos. Phys, vol.50, pp.1-3, 1992.

À. , F. Fang, C. C. London, S. 2az, U. K. Gallagher et al., Applied Modelling and Computation Group, Bristol Research Initiative for the Dynamic Global Environment, School of Geographical Sciences, p.2019