<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE article SYSTEM "http://www.the-cryosphere.net/inc/tc/copernicus.dtd">
<article language="en">
	<journal>
		<journal_title>The Cryosphere</journal_title>
		<journal_url>www.the-cryosphere.net</journal_url>
		<issn>1994-0416</issn>
		<eissn>1994-0424</eissn>
		<volume_number>1</volume_number>
		<issue_number>1</issue_number>
		<publication_year>2007</publication_year>
	</journal>
	<doi>10.5194/tc-1-41-2007</doi>
	<article_url>http://www.the-cryosphere.net/1/41/2007/</article_url>
	<abstract_html>http://www.the-cryosphere.net/1/41/2007/tc-1-41-2007.html</abstract_html>
	<fulltext_pdf>http://www.the-cryosphere.net/1/41/2007/tc-1-41-2007.pdf</fulltext_pdf>
	<start_page>41</start_page>
	<end_page>58</end_page>
	<publication_date>2007-11-22</publication_date>
	<article_title content_type="html">Using in-situ temperature measurements to estimate saturated soil thermal properties by solving a sequence of optimization problems</article_title>
	<authors>
		<author numeration="1" affiliations="1">
			<name>D. J. Nicolsky</name>
			<email>ftdjn@uaf.edu</email>
		</author>
		<author numeration="2" affiliations="1">
			<name>V. E. Romanovsky</name>
		</author>
		<author numeration="3" affiliations="2">
			<name>G. S. Tipenko</name>
		</author>
	</authors>
	<affiliations>
		<affiliation numeration="1" content_type="html">Geophysical Institute, University of Alaska Fairbanks, PO Box 757320, Fairbanks, AK 99775, USA</affiliation>
		<affiliation numeration="2" content_type="html">Institute of Environmental Geoscience Russian Academy of Sciences, 13-2 Ulansky pereulok, PO Box 145, Moscow, Russia</affiliation>
	</affiliations>
	<abstract content_type="html">We describe an approach to find an initial approximation to the thermal
properties of soil horizons. This technique approximates thermal
conductivity, porosity, unfrozen water content curves in horizons where no
direct temperature measurements are available. To determine physical
properties of ground material, optimization-based inverse techniques are
employed to fit the simulated temperatures to the measured ones. Two major
ingredients of these techniques are an algorithm to compute the soil
temperature dynamics and a procedure to find an initial approximation to the
ground properties. In this article we show how to determine the initial
approximation to the physical properties and present a new finite element
discretization of the heat equation with phase change to calculate the
temperature dynamics in soil. We successfully apply the proposed algorithm to
recover the soil properties for the Happy Valley site in Alaska using
one-year temperature dynamics. The determined initial approximation is
utilized to simulate the temperature dynamics over several consecutive years;
the difference between simulated and measured temperatures lies within
uncertainties of measurements.</abstract>
	<references>
		<reference numeration="1" content_type="text"> ACIA: Impacts of a Warming Arctic: Arctic Climate Impact Assessment, Cambridge University Press, 139 pp., 2004. </reference>
		<reference numeration="2" content_type="text"> Alifanov, O.: Inverse Heat Transfer Problems, Springer, Berlin, 348 pp., 1995. </reference>
		<reference numeration="3" content_type="text"> Alifanov, O., Artyukhin, E., and Rumyantsev, S.: Extreme Methods for Solving Ill-Posed Problems with Application to Inverse Heat Transfer Problems, Begell House, New York, 306 pp., 1996. </reference>
		<reference numeration="4" content_type="text"> Andersland, O. and Anderson, D.: Geotechnical Engineering for Cold Regions, McGraw-Hill, 566 pp., 1978. </reference>
		<reference numeration="5" content_type="text"> Anderson, D. and Morgenstern, N.: Physics, chemistry and mechanics of frozen ground: a review, in: Proceedings of the 2nd International Conference on Permafrost, Yakutsk, USSR, 257&amp;ndash;288, 1973. </reference>
		<reference numeration="6" content_type="text"> Avriel, M.: Nonlinear Programming: Analysis and Methods, Dover Publications, 554 pp., 2003. </reference>
		<reference numeration="7" content_type="text"> Bazaraa, M., Sherali, H., and Shetty, C M.: Nonlinear Programming: Theory and Algorithms, 2nd edn., John Wiley &amp; Sons, 1993. </reference>
		<reference numeration="8" content_type="text"> Boike, J. and Roth, K.: Time domain re¯ectometry as a field method for measuring water content and soil water electrical conductivity at a continuous permafrost site, Permafrost Periglac., 8, 359&amp;ndash;370, 1997. </reference>
		<reference numeration="9" content_type="text"> Brown, J., Ferrians, O., Heginbottom, J J., and Melnikov, E.: Circum-Arctic map of permafrost and ground-ice conditions, U.S. Geological Survey Circum-Pacific Map CP-45, 1:10 000 000, reston, Virginia, 1997. </reference>
		<reference numeration="10" content_type="text"> Carslaw, H. and Jaeger, J.: Conduction of Heat in Solids, Oxford University Press, London, 520 pp., 1959. </reference>
		<reference numeration="11" content_type="text"> Carson, J.: Analysis of soil and air temperatures by Fourier techniques, J. Geophys. Res., 68, 2217&amp;ndash;2232, 1963. </reference>
		<reference numeration="12" content_type="text"> Ciarlet, P.: The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 530 pp., 2002. </reference>
		<reference numeration="13" content_type="text"> Comini, G., Giudice, S D., Lewis, R., and Zienkiewicz, O.: Finite element solution of non-linear heat conduction problems with special reference to phase change, Int. J. Numer. Meth. Eng., 8, 613&amp;ndash;624, 1974. </reference>
		<reference numeration="14" content_type="text"> Dalhuijsen, A. and Segal, A.: Comparison of finite element techniques for solidification problems, Int. J. Numer. Meth. Eng., 23, 1807&amp;ndash;1829, 1986. </reference>
		<reference numeration="15" content_type="text"> de~Vries, D.: Physics of the Plant Environment, chap. Thermal properties of soils, edited by: van Wijk, W. R., Wiley, New York, 210&amp;ndash;235, 1963. </reference>
		<reference numeration="16" content_type="text"> Dennis, J. and Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, 394 pp., 1987. </reference>
		<reference numeration="17" content_type="text"> Fletcher, R.: Practical Methods of Optimization, John Wiley &amp; Sons, 450 pp., 2000. </reference>
		<reference numeration="18" content_type="text"> Galushkin, Y.: Numerical simulation of permafrost evolution as a part of sedimentary basin modeling: permafrost in the Pliocene-Holocene climate history of the Urengoy field in the West Siberian basin, Can. J. Earth Sci., 34, 935&amp;ndash;948, 1997. </reference>
		<reference numeration="19" content_type="text"> Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, 432 pp., 1989. </reference>
		<reference numeration="20" content_type="text"> Goodrich, W.: The influence of snow cover on the ground thermal regime, Can. Geotech. J., 19, 421&amp;ndash;432, 1982. </reference>
		<reference numeration="21" content_type="text"> Gupta, S.: The Classical Stefan Problem, Elsevier, Amsterdam, 404 pp., 2003. </reference>
		<reference numeration="22" content_type="text"> Hinkel, K.: Estimating seasonal values of thermal diffusivity in thawed and frozen soils using temperature time series, Cold Reg. Sci. Technol., 26, 1&amp;ndash;15, 1997. </reference>
		<reference numeration="23" content_type="text"> Hinzman, L., Kane, D., Gleck, R., and Everett, K.: Hydrological and thermal properties of the active layer in the Alaskan Arctic, Cold Reg. Sci. Technol., 19, 95&amp;ndash;110, 1991. </reference>
		<reference numeration="24" content_type="text"> Hobbs, P.: Ice Physics, Claredon Press, Oxford, 856 pp., 1974. </reference>
		<reference numeration="25" content_type="text"> Hurley, S. and Wiltshire, R J.: Computing thermal diffusivity from soil temperature measurements, Computers and Geosciences, 19, 475&amp;ndash;477, 1993. </reference>
		<reference numeration="26" content_type="text"> Jaeger, J C. and Sass, J H.: A line source method for measuring the thermal conductivity and diffusivity of cylindrical specimens of rock and other poor conductors, J. Appl. Phys., 15, 1187&amp;ndash;1194, 1964. </reference>
		<reference numeration="27" content_type="text"> Javierre, E., Vuik, C., Vermolen, F., and van~der Zwaag, S.: A comparison of numerical models for one-dimensional Stefan problems, J. Comput. Appl. Math., 192, 445&amp;ndash;459, 2006. </reference>
		<reference numeration="28" content_type="text"> Kane, D., Hinzman, L., and Zarling, J.: Thermal response of the active layer in a permafrost environment to climatic warming, Cold Reg. Sci. Technol., 19, 111&amp;ndash;122, 1991. </reference>
		<reference numeration="29" content_type="text"> Kane, D., Hinkel, K., Goering, D., Hinzman, L., and Outcalt, S.: Non-conductive heat transfer associated with frozen soils, Global Planet. Change, 29, 275&amp;ndash;292, 2001. </reference>
		<reference numeration="30" content_type="text"> Kolmogorov, A. and Fomin, S.: Introductory Real Analysis, Prentice-Hall, New York, 403 pp., 1975. </reference>
		<reference numeration="31" content_type="text"> Lagarias, J., Reeds, J., Wright, M., and Wright, P.: Convergence properties of the Nelder-Mead simplex method in low dimension, SIAM J. Optimiz., 9, 112&amp;ndash;147, 1998. </reference>
		<reference numeration="32" content_type="text"> Lemmon, E.: Numerical Methods in Thermal Problems, chap. Phase change technique for finite element conduction code, edited by: Lewis, R. W. and Morgan, K.,  Pineridge Press, Swansea, UK, 149&amp;ndash;158, 1979. </reference>
		<reference numeration="33" content_type="text"> Ling, F. and Zhang, T.: Impact of the timing and duration of seasonal snow cover on the active layer and permafrost in the Alaskan Arctic, Permafrost Periglac., 14, 141&amp;ndash;150, 2003. </reference>
		<reference numeration="34" content_type="text"> Lovell, C.: Temperature effects on phase composition and strength of partially frozen soil, Highway Research Board Bulletin, 168, 74&amp;ndash;95, 1957. </reference>
		<reference numeration="35" content_type="text"> Lunardini, V.: Freezing of soil with an unfrozen water content and variable thermal properties, CRREL Report 88-2, US Army Cold Regions Research and Engineering Lab, 30 pp., 1987. </reference>
		<reference numeration="36" content_type="text"> \mboxMÃ¶lders, N. and Romanovsky, V.: Long-term evaluation of \mboxHTSVS frozen ground/permafrost component using observations at Barrow, Alaska., J. Geophys. Res., 111, D04105, doi:10.1029/2005JD005957, 2006. </reference>
		<reference numeration="37" content_type="text"> \mboxThermal Logic: Thermal conductivity sensor user&apos;s manual, PO Box 781, Pullman, WA, 99163, 3 edn., 25 pp., 2001. </reference>
		<reference numeration="38" content_type="text"> McGaw, R W., Outcalt, S I., and Ng, E.: Thermal properties of wet tundra soils at Barrow, Alaska, in: Proceedings of 3rd International Conference on Permafrost, vol 1, National Research Council of Canada, Ottawa, Canada, 47&amp;ndash;53, 1978. </reference>
		<reference numeration="39" content_type="text"> Morgan, K., Lewis, R., and Zienkiewicz, O.: An improved algorithm for heat conduction problems with phase change, Int. J. Numer. Meth. Eng., 12, 1191&amp;ndash;1195, 1978. </reference>
		<reference numeration="40" content_type="text"> Mundim, M. and Fortes, M.: Numerical Methods in Thermal Problems, vol 6, chap. Evaluation of finite element method utilized in the solution of solid-liquid phase change problems, edited by: Lewis, R. W. and Morgan, K., Pineridge Press, Swansea, UK, 90&amp;ndash;100, 1979. </reference>
		<reference numeration="41" content_type="text"> Nelson, F. and Outcalt, S.: Anthropogenic geomorphology in northern Alaska, Polar Geography, 3, 17&amp;ndash;48, 1987. </reference>
		<reference numeration="42" content_type="text"> Oleson, K., Dai, Y., Bonan, G., Bosilovich, M., Dickinson, R., Dirmeyer, P., Hoffman, F., Houser, P., Levis, S., Niu, G.-Y., Thornton, P., Vertenstein, M., Yang, Z.-L., and Zeng, X.: Technical description of the Community Land Model (\mboxCLM), \mboxNCAR tech. note \mboxNCAR/TN-461+STR, NCAR, 173 pp., 2004. </reference>
		<reference numeration="43" content_type="text"> Osterkamp, T. and Romanovsky, V.: Characteristics of changing permafrost temperatures in the Alaskan Arctic, USA, Arctic Alpine Res., 28, 267&amp;ndash;273, 1996. </reference>
		<reference numeration="44" content_type="text"> Osterkamp, T. and Romanovsky, V.: Freezing of the active layer on the coastal plain of the Alaskan Arctic, Permafrost Periglac., 8, 23&amp;ndash;44, 1997. </reference>
		<reference numeration="45" content_type="text"> Permyakov, P.: Methods of determining the characteristics of dispersed media at a phase transition, Russian Physics Journal, 47(3), 240&amp;ndash;246, 2004. </reference>
		<reference numeration="46" content_type="text"> Pham, Q.: Comparison of general-purpose finite element methods for the Stefan problem, Numer. Heat Tr. B-Fund., 27, 417&amp;ndash;435, 1995. </reference>
		<reference numeration="47" content_type="text"> Pinder, G. and Gray, W.: Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, New York, 295 pp., 1977. </reference>
		<reference numeration="48" content_type="text"> Rank, E., Katz, C., and Werner, H.: On the importance of the discrete maximum principle in transient analysis using finite element methods, Int. J. Numer. Meth. Eng., 19, 1771&amp;ndash;1782, 1983. </reference>
		<reference numeration="49" content_type="text"> Robert, C. and Casella, G.: Monte Carlo Statistical Methods, Springer-Verlag, 645 pp., 2004. </reference>
		<reference numeration="50" content_type="text"> Romanovsky, V. and Osterkamp, T.: Interannual variations of the thermal regime of the active layer and near-surface permafrost in Northern Alaska, Permafrost Periglac., 6, 313&amp;ndash;335, 1995. </reference>
		<reference numeration="51" content_type="text"> Romanovsky, V. and Osterkamp, T.: Thawing of the active layer on the coastal plain of the Alaskan Arctic, Permafrost Periglac., 8, 1&amp;ndash;22, 1997. </reference>
		<reference numeration="52" content_type="text"> Romanovsky, V. and Osterkamp, T.: Effects of unfrozen water on heat and mass transport processes in the active layer and permafrost, Permafrost Periglac., 11, 219&amp;ndash;239, 2000. </reference>
		<reference numeration="53" content_type="text"> Samarskii, A. and Vabishchevich, P.: Computational Heat Transfer, Mathematical Modeling, vol 1, Wiley, 418 pp., 1996. </reference>
		<reference numeration="54" content_type="text"> Sass, J., Lachenbruch, A., and Munroe, R.: Thermal conductivity of rocks from measurements on fragments and its application to heat-flow determinations, J. Geophys. Res., 76, 3391&amp;ndash;3401, 1971. </reference>
		<reference numeration="55" content_type="text"> Sazonova, T., Romanovsky, V., Walsh, J., and Sergueev, D.: Permafrost dynamics in the 20th and 21st centuries along the East Siberian transect, J. Geophys. Res., 109, D01108, doi:10.1029/2003JD003680, 2004. </reference>
		<reference numeration="56" content_type="text"> Schmugge, T., Jackson, T., and McKim, H.: Survey of methods for soil moisture determination, Water Resour. Res., 16, 961&amp;ndash;979, 1980. </reference>
		<reference numeration="57" content_type="text"> Smith, M. and Tice, A.: Measurement of the unfrozen water content of soils—comparison of \mboxNMR and \mboxTDR methods, CRREL Report 88-18, US Army Cold Regions Research and Engineering Lab, 16 pp., 1988. </reference>
		<reference numeration="58" content_type="text"> Stafford, J.: Remote, non-contact and in-situ measurement of soil moisture content: a review, J. Agr. Eng. Res., 14, 151&amp;ndash;172, 1988. </reference>
		<reference numeration="59" content_type="text"> Thacker, W.: The role of the Hessian matrix in fitting models to measurements, J. Geophys. Res., 94, 6177&amp;ndash;6196, 1989. </reference>
		<reference numeration="60" content_type="text"> Thacker, W. and Long, R.: Fitting dynamics to data, J. Geophys. Res., 93, 1227&amp;ndash;1240, 1988. </reference>
		<reference numeration="61" content_type="text"> Tice, A., Oliphant, J., Nakano, Y., and Jenkins, T.: Relationship between the ice and unfrozen water phases in frozen soil as determined by pulsed nuclear magnetic resonance and physical desorption data, CRREL Report 82-15, US Army Cold Regions Research and Engineering Lab, 12 pp., 1982. </reference>
		<reference numeration="62" content_type="text"> Tikhonov, A. and Samarskii, A.: Equations of Mathematical Physics, Pergamon, 776 pp., 1963. </reference>
		<reference numeration="63" content_type="text"> Tikhonov, A., Leonov, A., and Yagola, A. G.: Nonlinear Ill-Posed Problems, Chapman and Hall, London, 392 pp., 1996. </reference>
		<reference numeration="64" content_type="text"> Topp, G C., Davis, J L., and Annan, A P.: Electromagnetic determination of soil water content: measurements in coaxial transmission lines, Water Resour. Res., 16, 574&amp;ndash;582, 1980. </reference>
		<reference numeration="65" content_type="text"> Ulaby, F., Moore, R., and Fung, A.: Microwave Remote Sensing, Addison-Wesley, Reading, MA, Vol. II, 1064 pp., 1982. </reference>
		<reference numeration="66" content_type="text"> Voller, V. and Swaminathan, C.: Fixed grid techniques for phase change problems: a review, Int. J. Numer. Meth. Eng., 30, 875&amp;ndash;898, 1990. </reference>
		<reference numeration="67" content_type="text"> Watanabe, K. and Mizoguchi, M.: Amount of unfrozen water in frozen porous media saturated with solution, Cold Reg. Sci. Technol., 34, 103&amp;ndash;110, 2002. </reference>
		<reference numeration="68" content_type="text"> Williams, P.: Properties and behaviour of freezing soils, Tech. Rep 72, Norwegian Geotechnical Institute, 120 pp., 1967. </reference>
		<reference numeration="69" content_type="text"> Yershov, E.: General Geocryology, Cambridge University Press, Cambridge, 604 pp., 1998. </reference>
		<reference numeration="70" content_type="text"> Yoshikawa, K., Overduin, P., and Harden, J.: Moisture content measurements of moss (Sphagnum spp.) using commercial sensors, Permafrost Periglac., 15, 309&amp;ndash;318, 2004. </reference>
		<reference numeration="71" content_type="text"> Zhang, T. and Osterkamp, T E.: Considerations in determining the thermal diffusivity from temperature time series using finite difference methods, Cold Reg. Sci. Technol., 23, 333&amp;ndash;341, 1995. </reference>
		<reference numeration="72" content_type="text"> Zhuang, Q., Romanovsky, V., and McGuire, A.: Incorporation of a permafrost model into a large-scale ecosystem model: evaluation of temporal and spatial scaling issues in simulating soil thermal dynamics, J. Geophys. Res., 106, 33 649&amp;ndash;33 670, 2001. </reference>
		<reference numeration="73" content_type="text"> Zienkiewicz, O. and Taylor, R.: The Finite Element Method, vol 1, McGraw-Hill, London, 470 pp., 1991. </reference>
	</references>
</article>
