Regional climate change signals inferred from a borehole temperature profile in Muli, Qilian Mountain, using the Tikhonov method

References

• Bartlett, M. G., D. S. Chapman, and R. N. Harris. 2004. Snow and the ground temperature record of climate change. Journal of Geophysical Research 109 (F4):F04008. doi:https://doi.org/10.1029/2004JF000224.
   Web of Science ®Google Scholar
• Beck, A. E. 1977. Climatically perturbed temperature gradients and their effect on regional and continental heat-flow measurements. Tectonophysics 41 (1–3):17–39. doi:https://doi.org/10.1016/0040-1951(77)90178-0.
   Google Scholar
• Birch, F. 1948. The effects of Pleistocene climatic variations upon geothermal gradients. American Journal of Science 246 (12):729–60. doi:https://doi.org/10.2475/ajs.246.12.729.
   Google Scholar
• Bodri, L., and V. Cermak. 2011. Borehole climatology: A new method on how to reconstruct climate. Amsterdam: Elsevier.
   Google Scholar
• Carslaw, H. S., and J. C. Jaeger. 1959. Conduction of heat in solids. 2nd ed. Oxford, UK: Oxford University Press.
   Google Scholar
• Clow, G. D. 1992. The extent of temporal smearing in surface-temperature histories derived from borehole temperature measurements. Global and Planetary Change 6 (2):81–86. doi:https://doi.org/10.1016/0921-8181(92)90027-8.
   Google Scholar
• Craven, P., and G. Wahba. 1978. Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik 31 (4):377–403. doi:https://doi.org/10.1007/BF01404567.
   Web of Science ®Google Scholar
• Dahl-Jensen, D., K. Mosegaard, N. Gundestrup, G. D. Clow, S. J. Johnsen, A. W. Hansen, and N. Balling. 1998. Past temperatures directly from the Greenland Ice Sheet. Science 282 (5387):268–71. doi:https://doi.org/10.1126/science.282.5387.268.
   PubMed Web of Science ®Google Scholar
• Engl, H. W., M. Hanke, and A. Neubauer. 1996. Regularization of inverse problems. Netherlands: Springer Science & Business Media.
   Google Scholar
• Fernando, J. S., P. Carolyne, B. Hugo, and M. Jean-Claude. 2016. North American regional climate reconstruction from ground surface temperature histories. Climate of the Past 12 (12):2181–94. doi:https://doi.org/10.5194/cp-12-2181-2016.
   Google Scholar
• Gosnold, W., P. Todhunter, and W. Schmidt. 1997. The borehole temperature record of climate warming in the mid-continent of North America. Global and Planetary Change 15 (1):33–45. doi:https://doi.org/10.1016/S0921-8181(97)00002-7.
   Web of Science ®Google Scholar
• Groetsch, C. W. 1984. The theory of Tikhonov regularization for Fredholm equations of the first kind. Boston, MA: Pitman (Advanced Publishing Program).
   Google Scholar
• Hansen, P. C. 1992a. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review 34:561–80. doi:https://doi.org/10.1137/1034115.
   Web of Science ®Google Scholar
• Hansen, P. C. 1992b. Numerical tools of analysis and solution of Fredholm integral equations of the first kind. Inverse Problems 8 (6):849–72. doi:https://doi.org/10.1088/0266-5611/8/6/005.
   Web of Science ®Google Scholar
• Hansen, P. C. 1993. Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms 14:1487–503.
   Google Scholar
• Hansen, P. C. 1996. Rank-deficient and discrete ill-posed problems. Lyngby, Denmark: Technical University of Denmark.
   Google Scholar
• Hansen, P. C. 2000. The L-curve and its use in the numerical treatment of inverse problem. In Computational inverse problems in electrocardiology. Advances in computational bioengineering series, ed. P. Johnston, vol. 4, 119–142. Southampton: WIT Press.
   Google Scholar
• Hansen, P. C., and D. P. O’Leary. 1993. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal on Scientific Computing 14 (6):1487–503. doi:https://doi.org/10.1137/0914086.
   Web of Science ®Google Scholar
• Harris, R. N., and D. S. Chapman. 2001. Mid-latitude (30°N-60°N) climatic warming inferred by combining borehole temperatures with surface air temperatures. Geophysical Research Letters 28 (5):747–50. doi:https://doi.org/10.1029/2000GL012348.
   Google Scholar
• Harris, R. N., and D. S. Chapman. 2005. Borehole temperatures and tree rings: Seasonality and estimates of extratropical Northern Hemispheric warming. Journal of Geophysical Research Earth Surface 110 (F4):F04003.
   Web of Science ®Google Scholar
• Holmes, J. A., E. R. Cook, and B. Yang. 2009. Climate change over the past 2000 years in Western China. Quaternary International 194 (1–2):0–107. doi:https://doi.org/10.1016/j.quaint.2007.10.013.
   Google Scholar
• Hon, Y. C., and T. Wei. 2004. A fundamental solution method for inverse heat conduction problem. Engineering Analysis with Boundary Elements 28 (5):489–95. doi:https://doi.org/10.1016/S0955-7997(03)00102-4.
   Web of Science ®Google Scholar
• Hu, Q. 2005. How have soil temperatures been affected by the surface temperature and precipitation in the Eurasian continent? Geophysical Research Letters 32 (14):L14711. doi:https://doi.org/10.1029/2005GL023469.
   Web of Science ®Google Scholar
• Huang, S., and H. N. Pollack. 1998. Global borehole temperature database for climate reconstruction. IGBP Pages/World Data Center—A for Paleoclimatology data contribution Series No. 1998-044. Boulder, CO: NOAA/NGDC Paleoclimatology Program.
   Google Scholar
• Huang, S., H. N. Pollack, and P. Y. Shen. 2000. Temperature trends over the past five centuries reconstructed from borehole temperatures. Nature 403 (6771):756–58. doi:https://doi.org/10.1038/35001556.
   Google Scholar
• Jackson, D. D. 1972. Interpretation of inaccurate, insufficient, and inconsistent data. Geophysical Journal International 28 (2):97–110. doi:https://doi.org/10.1111/j.1365-246X.1972.tb06115.x.
   Google Scholar
• Lachenbruch, A. H., and B. V. Marshall. 1986. Changing climate: Geothermal evidence from permafrost in Alaska. Science 234 (4777):689–96. doi:https://doi.org/10.1126/science.234.4777.689.
   Web of Science ®Google Scholar
• Lanczos, C. 1961. Linear differential operators. New York: D. van Nostrand.
   Google Scholar
• Lawson, C. L., and R. J. Hanson. 1995. Solving least squares problems. SIAM. Philadelphia, PA: First published by Prentice-Hall.
   Google Scholar
• Liu, J., and T. Zhang. 2014. Fundamental solution method for reconstructing past climate change from borehole temperature gradients. Cold Regions Science and Technology 102:32–40. doi:https://doi.org/10.1016/j.coldregions.2014.02.005.
   Web of Science ®Google Scholar
• Liu, J., T. Zhang, E. Jafarov, and G. D. Clow. Submitted. Application of Tikhonov regularization to reconstruct past climate record from borehole temperature: Synthetic cases.
   Google Scholar
• Majorowicz, J., S. E. Grasby, G. Ferguson, J. Safanda, and W. Skinner. 2006. Paleoclimatic reconstructions in western Canada from borehole temperature logs: Surface air temperature forcing and groundwater flow. Climate of the Past 2 (1):1–10. doi:https://doi.org/10.5194/cp-2-1-2006.
   Google Scholar
• Mann, M. E., S. Rutherford, R. S. Bradley, M. K. Hughes, and F. T. Keimig. 2003. Optimal surface temperature reconstructions using terrestrial borehole data. Journal of Geophysical Research 108 (D7):4203. doi:https://doi.org/10.1029/2002JD002532.
   Google Scholar
• Mareschal, J. C., and H. Beltrami. 1992. Evidence for recent warming from perturbed geothermal gradients: Examples from eastern Canada. Climate Dynamics 6 (3):135–43. doi:https://doi.org/10.1007/BF00193525.
   Google Scholar
• Menke, W., 1989. Geophysical data analysis. International Geophysical Series 45. San Diego: Academic Press.
   Google Scholar
• Pollack, H. N., and S. Huang. 2000. Climate reconstructions from subsurface temperatures. Annual Review of Earth and Planetary Sciences 28 (1):339–65. doi:https://doi.org/10.1146/annurev.earth.28.1.339.
   Google Scholar
• Pollack, H. N., S. Huang, and P.-Y. Shen. 1998. Climate change record in subsurface temperatures: A global perspective. Science 282 (5387):279–81. doi:https://doi.org/10.1126/science.282.5387.279.
   PubMed Web of Science ®Google Scholar
• Pollack, H. N., J. E. Smerdon, and P. E. Keken. 2005. Variable seasonal coupling between air and ground temperatures: A simple representation in terms of subsurface thermal diffusivity. Geophysical Research Letters 32 (15):L15405. doi:https://doi.org/10.1029/2005GL023869.
   Web of Science ®Google Scholar
• Rath, V., and D. Mottaghy. 2007. Smooth inversion for ground surface temperature histories: Estimating the optimum regularization parameter by generalized cross-validation. Geophysical Journal International 171 (3):1440–48. doi:https://doi.org/10.1111/j.1365-246X.2007.03587.x.
   Google Scholar
• Shen, Y., J. Liu, and S. Zhao. 2012. Long-term stability of thermometric thermistor sensor SKLFSE-TS used at low temperature. Journal of Glaciology and Geocryology 34 (4):891–97.
   Google Scholar
• Smerdon, J. E., H. Beltrami, C. Creelman, and M. B. Stevens. 2009. Characterizing land surface processes: A quantitative analysis using air‐ground thermal orbits. Journal of Geophysical Research: Atmospheres (1984–2012) 114 (D15). doi:https://doi.org/10.1029/2009JD011768.
   Google Scholar
• Smerdon, J. E., H. N. Pollack, V. Cermak, J. W. Enz, M. Kresl, J. Safanda, and J. F. Wehmiller. 2004. Air-ground temperature coupling and subsurface propagation of annual temperature signals. Journal of Geophysical Research: Atmospheres (1984-2012) 109 (D21). doi:https://doi.org/10.1029/2004JD005056.
   Google Scholar
• Smerdon, J. E., H. N. Pollack, V. Cermak, J. W. Enz, M. Kresl, J. Safanda, and J. F. Wehmiller. 2006. Daily, seasonal, and annual relationships between air and subsurface temperatures. Journal of Geophysical Research: Atmospheres (1984–2012) 111 (D7). doi:https://doi.org/10.1029/2004JD005578.
   Google Scholar
• Stieglitz, M., S. J. Dery, V. E. Romanovsky, and T. E. Osterkamp. 2003. The role of snow cover in the warming of arctic permafrost. Geophysical Research Letters 30 (13). doi:https://doi.org/10.1029/2003GL017337.
   Web of Science ®Google Scholar
• Tikhonov, A. N., and V. Y. Arsenin. 1979. Methods for solving ill-posed problems. Scripta series in mathematics. Moscow: Nauka.
   Google Scholar
• Vasseur, G., P. H. Bernard, J. Van de Meulebrouck, Y. Kast, and J. Jolivet. 1983. Holocene palaeotemperatures deduced from geothermal measurements. Palaeogeography, Palaeoclimatology, Palaeoecology 43 (3–4):237–59. doi:https://doi.org/10.1016/0031-0182(83)90013-5.
   Google Scholar
• Wahba, G., 1977. A survey of some smoothing problems andthe method of generalized cross-validation for solvingthem. In Applications of Statistics: Proceedings of the Symposium Held at Wright State University, Dayton, Ohio, 14–18 June 1976, P. R. Krishnaiah (Ed), 507–23. Amsterdam: Elsevier.
   Google Scholar
• Wu, Q., T. Zhang, and Y. Liu. 2010. Permafrost temperatures and thickness on the Qinghai-Tibet Plateau. Global and Planetary Change 72 (1):32–38. doi:https://doi.org/10.1016/j.gloplacha.2010.03.001.
   Google Scholar
• Wu, Q., T. Zhang, and Y. Liu. 2012. Thermal state of the active layer and permafrost along the Qinghai-Xizang (Tibet) railway from 2006 to 2010. The Cryosphere 6 (3):607–12. doi:https://doi.org/10.5194/tc-6-607-2012.
   Web of Science ®Google Scholar
• Yang, B., A. Brauning, and S. Yafeng. 2003. Late Holocene temperature fluctuations on the Tibetan Plateau (EI). Quaternary Science Reviews 22 (21):2335–44. doi:https://doi.org/10.1016/S0277-3791(03)00132-X.
   Google Scholar
• Yao, T., L. G. Thompson, V. Mosbrugger, F. Zhang, Y. Ma, T. Luo, B. Xu, X. Yang, D. R. Joswiak, W. Wang, et al. 2012. Third pole environment (TPE). Environmental Development 3:52–64. doi:https://doi.org/10.1016/j.envdev.2012.04.002.
   Google Scholar
• Zhang, Y., H. Shugui, and P. Hongxi. 2012. Preliminary study on spatiotemporal pattern of climate change over Tibet Plateau during past millennium. Marine Geology & Quaternary Geology 32 (3):135–146.
   Google Scholar