A robust and energy-conserving model of freezing variably-saturated soil

Cryosphere

Volumn 5, Issue 2, 2011, Pages 469-484

  Dall'Amico, M ^a,c   Endrizzi, S ^b   Gruber, S ^b   Rigon, R ^a  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c Mountain eering Srl   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY CONSERVATION; FREEZING; FROZEN GROUND; NONLINEARITY; RICHARDS EQUATION; THAWING; UNSATURATED MEDIUM; WATER FLOW;

EID: 79958148808     PISSN: 19940416     EISSN: 19940424     Source Type: Journal    
DOI: 10.5194/tc-5-469-2011     Document Type: Article

References (40)

1. Anisimov, O., Shiklomanov, N., and Nelson, E.: Variability of seasonal thaw depth in permafrost regions: A stochastic modeling approach, Ecol. Model., 153,217-227, 2002. (Pubitemid 34780406)
2. Brooks, R. H. and Corey, A. T.: Hydraulic properties of porous me-dia, Hydrology paper, 3, colorado State University, Fort Collins, 1964.
3. Carslaw, H. and Jaeger, J.: Conduction of heat in solids, Clarendon Press Oxford, 1959.
4. Christoffersen, P., and Tulaczyk, S.: Response ofsubglacial sedi-ments to basal freeze-on: 1. Theory and comparison to observa-tions from beneath the West Antarctica Ice Sheet, J. Geophys. Res, 108,2222,doi:10.1029/2002JB001935, 2003.
5. Clapp, R. B. and Hornberger, G. M.: Empirical equations for some hydraulic properties, Water Resour. Res., 14, 601-605, 1978.
6. Conte, S. and De Boor, C.: Elementary numerical analysis: an al-gorithmic approach, McGraw-Hill Higher Education, 1980.
7. Daanen, R., Misra, D., and Epstein, H.: Active-Layer Hydrology in Nonsorted Circle Ecosystems of the Arctic Tundra, Vadose Zone J., 6(4), 694-704,2007. (Pubitemid 350232064)
8. Dall'Amico, M.: Coupled water and heat transfer in permafrost modeling, Ph.D. thesis, Institute ofCivil and Environmental En-gineering, Universita' degli Studi di Trento, Trento, available at: http://eprints-phd.biblio.unitn.it/ 335/, 2010.
9. Endrizzi, S., Quinton, W. L., and Marsh, P.: Modelling the spatial pattern ofground thaw in a small basin in the arctic tundra, The Cryosphere Discuss., 5, 367-400, doi:10.5194/tcd-5-367-2011, 2011.
10. Farouki, O. T.: The thermal properties of soils in cold regions, Cold Reg. Sci. Technol., 5, 67-75, 1981.
11. Fuchs, M., Campbell, G., and Papendick, R.: An analysis ofsensi-ble and latent heat flow in a partially frozen unsaturated soil, Soil Sci. Soc. Am. J., 42(3), 379-385, 1978. (Pubitemid 8620757)
12. Gardner, W.: Some steady-state solutions of the unsaturated mois-ture flow equation with application to evaporation from a water table, Soil Sci., 85(4), 228-232, 1958.
13. Hansson, K., Simunek, J., Mizoguchi, M., Lundin, L., and van Genuchten, M.: Water Flow and Heat Transport in Frozen Soil Numerical Solution and Freeze-ThawApplications, Vadose Zone J., 3(2), 693-704, 2004.
14. Harlan, R.: Analysis of coupled heat-fluid transport in partially frozen soil, Water Resour. Res., 9(5), 1314-1323, 1973.
15. Jame, Y. and Norum, D.: Heat and mass transfer in a freezing un-saturated porous medium, Water Resour. Res., 16(4), 811-819, 1980.
16. Johansen, O.: Thermal conductivity of soils, Ph.D. thesis, Ph.D. dissertation, Norwegian Technical University, Trondheim, 1975.
17. Kelley, C.: Solving nonlinear equations withNewton's method, Society for Industrial Mathematics, 2003.
18. Lukianov, V. S. and Golovko, M. D.: Calculation of the depth offreeze in soils, Bull. 23., Union of Transp. Constr. Moscow. (English translation, National Technical Information Service, Springfield, Va.) 1957 (in Russian).
19. Lunardini, V.: Heat transfer in cold climates, Van Nostrand Rhein-hold, New York, 1981.
20. Luo, L., Robock, A., Vinnikov, K. Y., et al.: Effects of frozen soil on soil temperature, spring infiltration, and runoff: Results from the PILPS 2 (d) experiment at Valdai, Russia, J. Hydrometeorol., 4(2), 334-351,2003. (Pubitemid 36751428)
21. McKenzie, J., Voss, C., and Siegel, D.: Groundwater flow with energy transport and water-ice phase change: Numerical simula-tions, benchmarks, and application to freezing in peat bogs, Adv. Water Resour., 30(4), 966-983,2007.
22. Mikkola, M. and Hartikainen, J.: Mathematical model ofsoil freez-ing and its numerical implementation, Int. J. Numer. Meth. Eng., 52(5-6), 543-557,2001. (Pubitemid 32944195)
23. Miller, R.: Phase equilibria and soil freezing, in: Permafrost: Pro-ceedings of the Second International Conference. Washington DC: National Academy of Science-National Research Council, 287, 193-197, 1965.
24. Mualem, Y.: A new model for predicting the hydraulic conductivity ofunsaturated porous media, Water Resour. Res., 12, 513-522, 1976.
25. Nakano, Y. and Brown, J.: Effect of a freezing zone offinite width on thermal regime of soils, Water Resour. Res., 5, 1226-1233, 1971.
26. Newman, G. and Wilson, G.: Heat and mass transfer in unsaturated soils during freezing, Can. Geotech. J., 34(1), 63-70, 1997.
27. Rigon, R., Bertoldi, G., and Over, T. M.: GEOtop: a distributed hydrological model with coupled water and energy budgets, J. Hydrometeorol., 7,371-388,2006. (Pubitemid 44070409)
28. Schaap, M., Leij, F., and van Genuchten, M.: Rosetta: a com-puter program for estimating soil hydraulic parameters with hierarchical pedotransfer functions, J. Hydrol., 251(3-4), 163-176,2001. (Pubitemid 32792750)
29. Shoop, S. and Bigl, S.: Moisture migration during freeze and thaw ofunsaturated soils: modeling and large scale experiments, Cold Reg. Sci. Technol., 25(1), 33-45, 1997.
30. Smirnova, T., Brown, J., Benjamin, S., and Kim, D.: Parameteriza-tion of cold-season processes in the MAPS land-surface scheme, J. Geophys. Res., 105(D3), 4077-4086, 2000.
31. Spaans, E. and Baker, J.: The Soil Freezing Characteristic: Its Mea-surement and Similarity to the Soil Moisture Characteristic, Soil Sci. Soc. Am. J., 60(1), 13-19, 1996.
32. Tomita, H.: Analysis of Spurious Surface Temperature at the Atmosphere-Land Interface and a New Method to Solve the Sur-face Energy Balance Equation, J. Hydrometeorol., 10(3), 833-844,2009.
33. Van Genuchten, M. T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898, 1980.
34. Viterbo, P., Beljaars, A., Mahfouf, J., and Teixeira, J.: The rep-resentation of soil moisture freezing and its impact on the stable boundary layer, Q. J. Roy. Meteorol. Soc., 125(559), 2401-2426, 1999. (Pubitemid 30024882)
35. Watanabe, K.: Water and heat flow in a directionally frozen silty soil, Proceedings of the third HYDRUS Workshop, 28 June 2008, Tokyo University of Agriculture and Technology, Tokyo, Japan, ISBN 978-4-9901192, 15-22,2008.
36. Watanabe, K. and Mizoguchi, M.: Amount of unfrozen water in frozen porous media saturated with solution, Cold Reg. Sci. Technol., 34(2), 103-110,2002. (Pubitemid 34466087)
37. Williams, P. and Smith, M.: The frozen earth: fundamentals of geocryology, Cambridge University Press, 1989.
38. Zhang, X., Sun, S., and Xue, Y.: Development and testing of a frozen soil parameterization for cold region studies, J. Hydrom-eteorol., 8(4), 690-701,2007. (Pubitemid 47491195)
39. Zhang, Y., Carey, S., and Quinton, W.: Evaluation of the al-gorithms and parameterizations for ground thawing and freezing simulation in permafrost regions, J. Geophys. Res, 113, D17116, doi:10.1029/2007JD009343,2008.
40. Zhao, L., Gray, D., and Male, D.: Numerical analysis of simultaneous heat and mass transfer during infiltration into frozen ground, J. Hydrol., 200(1-4), 345-363, 1997. (Pubitemid 28050189)