TC The Cryosphere TC The Cryosphere 1994-0424 Copernicus Publications Göttingen, Germany 10.5194/tc-5-741-2011 Modeling the thermal dynamics of the active layer at two contrasting permafrost sites on Svalbard and on the Tibetan Plateau Weismüller J. 1 4 Wollschläger U. 1 5 6 Boike J. 2 Pan X. 1 Yu Q. 3 Roth K. 1 Institute of Environmental Physics, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany Alfred Wegener Institute for Polar and Marine Research – Research Unit Potsdam, Telegrafenberg A 43, 14473 Potsdam, Germany Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 260 Donggang West Road, 730000 Lanzhou, China now at: Department of Earth and Environmental Sciences, Geophysics Section, Ludwig-Maximilians University, Theresienstr. 41, 80333 Munich, Germany now at: UFZ – Helmholtz Centre for Environmental Research, Permoserstr. 15, 04318 Leipzig, Germany now at: WESS – Water and Earth System Science Competence Cluster, Keplerstr. 17, 72074 Tübingen, Germany 19 09 2011 5 3 741 757 Copyright: © 2011 J. Weismüller et al. 2011 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://tc.copernicus.org/articles/5/741/2011/tc-5-741-2011.html The full text article is available as a PDF file from https://tc.copernicus.org/articles/5/741/2011/tc-5-741-2011.pdf

Employing a one-dimensional, coupled thermal and hydraulic numerical model, we quantitatively analyze high-resolution, multi-year data from the active layers at two contrasting permafrost sites. The model implements heat conduction with the de Vries parameterization, heat convection with water and vapor flow, freeze-thaw transition parameterized with a heuristic soil-freezing characteristic, and liquid water flow with the Mualem-van Genuchten parameterization. The model is driven by measured temperatures and water contents at the upper and lower boundary with all required material properties deduced from the measured data. The aims are (i) to ascertain the applicability of such a rather simple model, (ii) to quantify the dominating processes, and (iii) to discuss possible causes of remaining deviations. <br><br> Soil temperatures and water contents as well as characteristic quantities like thaw depth and duration of the isothermal plateau could be reproduced. Heat conduction is found to be the dominant process by far at both sites, with non-conductive transport contributing a maximum of some 3% to the mean heat flux at the Spitsbergen site, most of the time very much less, and practically negligible at the Tibetan site. Hypotheses discussed to explain the remaining deviations between measured and simulated state variables include, besides some technical issues, infiltration of snow melt, dry cracking with associated vapor condensation, and mechanical soil expansion in detail.

 References Bittelli,&nbsp;M., Ventura,&nbsp;F., Campbell,&nbsp;G., Snyder,&nbsp;R., Gallegati,&nbsp;F., and Pisa,&nbsp;P.: Coupling of heat, water vapor, and liquid water fluxes to compute evaporation in bare soils, J. Hydrol., 362, 191–205, 2008. Boike, J., Roth, K., and Ippisch, O.: Seasonal snow cover on frozen ground: Energy balance calculations of a permafrost site near Ny-Ålesund, Spitsbergen, J. Geophys. Res., 108, 8163, <a href="http://dx.doi.org/10.1029/2001JD000939">https://doi.org/10.1029/2001JD000939</a>, 2003. Boike,&nbsp;J., Ippisch,&nbsp;O., Overduin,&nbsp;P., Hagedorn,&nbsp;B., and Roth,&nbsp;K.: Water, heat and solute dynamics of a mud boil, {S}pitsbergen, Geomorphology, 95, 61–73, 2008. Buck,&nbsp;A.: New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol., 20, 1527–1532, 1981. Carslaw,&nbsp;H. and Jaeger,&nbsp;J.: Conduction of Heat in Solids, chap.&nbsp;XI, Oxford University Press, 2nd edn., 287–288, 1959. Christoffersen, P. and Tulaczyk, S.: Response of subglacial sediments to basal freeze-on, 1 Theory and comparison to observations from beneath the West Antarctic Ice Sheet, J. Geophys. Res., 108, 2222, <a href="http://dx.doi.org/10.1029/2002JB001935">https://doi.org/10.1029/2002JB001935</a>, 2003. COMSOL Multiphysics: Version 3.5a, 3 December 2008, <a href="http://www.comsol.com/">http://www.comsol.com/</a>, last access: 14 September 2011, 2008. Daanen,&nbsp;R., Misra,&nbsp;D., and Epstein,&nbsp;H.: Active-layer hydrology in nonsorted circle ecosystems of the Arctic Tundra, Vadose Zone J., 6, 694–704, 2007. Davis&nbsp;T.&nbsp;A.: Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method, ACM T. Math. Software, 30, 196–199, 2004 Deuflhard,&nbsp;P.: A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, Numer. Math., 22, 289–315, 1974. de&nbsp;Vries,&nbsp;D.: Transfer processes in the plant environment, in: Heat and Mass Transfer in the Biosphere, Wiley and Sons, New York, 5–28, 1975. Engelmark,&nbsp;H. and Svensson,&nbsp;U.: Numerical modelling of phase change in freezing and thawing unsaturated soil, Nord. Hydrol., 24, 95–110, 1993. Gasse,&nbsp;F., Arnold,&nbsp;M., Fontes,&nbsp;J., Fort,&nbsp;M., Gibert,&nbsp;E., Huc,&nbsp;A., Bingyan,&nbsp;L., Yuanfang,&nbsp;L., Qing,&nbsp;L., Melieres,&nbsp;F., Campo,&nbsp;E.&nbsp;V., Fubao,&nbsp;W., and Qingsong,&nbsp;Z.: A 13 000-year climate record from Western {T}ibet, Nature, 353, 742–745, 1991. Guymon,&nbsp;G. and Luthin,&nbsp;J.: A&nbsp;coupled heat and moisture transport model for arctic soils, Water Resour. Res., 10, 995–1001, 1974. Hansson,&nbsp;K., {Š}im{ů}nek,&nbsp;J., Mizoguchi,&nbsp;M., Lundin,&nbsp;L., and van Genuchten,&nbsp;M.&nbsp;T.: Water flow and heat transport in frozen soil: numerical solution and freeze-thaw applications, Vadose Zone J., 3, 693–704, 2004. Harlan,&nbsp;R.: Analysis of coupled heat-fluid transport in partially frozen soil, Water Resour. Res., 9, 1314–1323, 1973. Harris,&nbsp;K., Haji-Sheikh,&nbsp;A., and Nnanna,&nbsp;A.&nbsp;A.: Phase-change phenomena in porous media – a&nbsp;non-local thermal equilibrium model, Int. J. Heat Mass Tran., 44, 1619–1625, 2001. Hindmarsh,&nbsp;A. C., Brown,&nbsp;P. N., Grant&nbsp;K. E., Lee,&nbsp;S. L., Serban&nbsp;R., Shumaker&nbsp;D. E., and Woodward,&nbsp;C. S., SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers, ACM T. Math. Software, 31, 363–396, 2005. Hinzman,&nbsp;L., Goering,&nbsp;D., and Kane,&nbsp;D.: A distributed thermal model for calculating soil temperature profiles and depth of thaw in permafrost regions, J. Geophys. Res., 103, 28975–28991, 1998. Ippisch,&nbsp;O., Cousin,&nbsp;I., and Roth,&nbsp;K.: {W}ärmeleitung in porösen {M}edien – {A}uswirkungen der {B}odenstruktur auf {W}ärmeleitung und {T}emperaturverteilung, Mitteilgn. Dtsch. Bodenkundl. Gesellsch., 87, 405–408, 1998. Kane,&nbsp;D., Hinzman,&nbsp;L., and Zarling,&nbsp;J.: Thermal response of the active layer to climatic warming in a permafrost environment, Cold Reg. Sci. Technol., 19, 111–122, 1991. Kane,&nbsp;D., Hinkel,&nbsp;K., Goering,&nbsp;D., Hinzman,&nbsp;L., and Outcalt,&nbsp;S.: Non-conductive heat transfer associated with frozen soils, Global Planet. Change, 29, 275–292, 2001. Li,&nbsp;S. and He,&nbsp;Y.: Features of permafrost in the {W}est {K}unlun {M}ountains, Bull. Glacier Res., 7, 161–167, 1989. Mualem,&nbsp;Y.: A&nbsp;new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12, 593–622, 1976. Murray,&nbsp;F.&nbsp;W.: On the computation of saturation vapor pressure, J. Appl. Meteorol., 6, 203–204, 1967. Nakano,&nbsp;Y. and Brown,&nbsp;J.: Effect of a freezing zone of finite width on the thermal regime of soils, Water Resour. Res., 7, 1226–1233, 1971. Philip,&nbsp;J.: Evaporation, and moisture and heat fields in the soil, J. Meteorol., 14, 354–366, 1957. Riseborough,&nbsp;D., Shiklomanov,&nbsp;N., Etzelm{ü}ller,&nbsp;B., Gruber,&nbsp;S., and Marchenko,&nbsp;S.: Recent advances in permafrost modelling, Permafrost Periglac., 19, 137–156, 2008. Romanovsky,&nbsp;V. and Osterkamp,&nbsp;T.: Thawing of the active layer on the coastal plain of the {A}laskan Arctic, Permafrost Periglac., 8, 1–22, 1997. Roth,&nbsp;K. and Boike,&nbsp;J.: Quantifying the thermal dynamics of a permafrost site near {N}y-{{\AA{}}}lesund, {S}valbard, Water Resour. Res., 37, 2901–2914, 2001. Šim{ů}nek,&nbsp;J., Huang,&nbsp;K., and van Genuchten,&nbsp;M.&nbsp;T.: The SWMS}_{3D code for simulating water flow and solute transport in three-dimensional variably-saturated media, V}ersion 1.0, Research Report No.&nbsp;139, US {S}alinity {L}aboratory, {A}gricultural {R}esearch {S}ervice, {US {D}epartment of {A}griculture, {R}iverside, {C}alifornia, 1995. van Genuchten,&nbsp;M.&nbsp;T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892–898, 1980. Wang, L., Koike, T., Yang, K., Jin, R., and Li, H.: Frozen soil parameterization in a distributed biosphere hydrological model, Hydrol. Earth Syst. Sci., 14, 557–571, <a href="http://dx.doi.org/10.5194/hess-14-557-2010">https://doi.org/10.5194/hess-14-557-2010</a>, 2010.