Abstract
Integrated surface/subsurface models for simulating the thermal hydrology of permafrost-affected regions in a warming climate have recently become available, but computational demands of those new process-rich simu- lation tools have thus far limited their applications to one-dimensional or small two-dimensional simulations. We present a mixed-dimensional model structure for efficiently simulating surface/subsurface thermal hydrology in low-relief permafrost regions at watershed scales. The approach replaces a full three-dimensional system with a two-dimensional overland thermal hydrology system and a family of one-dimensional vertical columns, where each column represents a fully coupled surface/subsurface thermal hydrology system without lateral flow. The system is then operator split, sequentially updating the overland flow system without sources and the one-dimensional columns without lateral flows. We show that the app- roach is highly scalable, supports subcycling of different processes, and compares well with the corresponding fully three-dimensional representation at significantly less computational cost. Those advances enable recently developed representations of freezing soil physics to be coupled with thermal overland flow and surface energy balance at scales of 100s of meters. Although developed and demonstrated for permafrost thermal hydrology, the mixed-dimensional model structure is applicable to integrated surface/subsurface thermal hydrology in general.
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Brown, J., Ferrians, Jr, O., Heginbottom, J., Melnikov, E.: Circum-Arctic map of permafrost and ground-ice conditions, pp. 45 (1997)
Jorgenson, M.T., Racine, C.H., Walters, J.C., Osterkamp, T.E.: Permafrost degradation and ecological changes associated with a warmingclimate in Central Alaska. Clim. Chang. 48, 551–579 (2001)
Schuur, E.A.G., McGuire, A.D., Schaedel, C., Grosse, G., Harden, J.W., Hayes, D.J., Hugelius, G., Koven, C.D., Kuhry, P., Lawrence, D.M., Natali, S.M., Olefeldt, D., Romanovsky, V.E., Schaefer, K., Turetsky, M.R., Treat, C.C., Vonk, J.E.: Climate change and the permafrost carbon feedback. Nature 520, 171–179 (2015)
Hugelius, G., Strauss, J., Zubrzycki, S., Harden, J.W., Schuur, E.A.G., Ping, C.-L. , Schirrmeister, L., Grosse, G., Michaelson, G.J., Koven, C.D., O’Donnell, J.A., Elberling, B., Mishra, U., Camill, P., Yu, Z., Palmtag, J., Kuhry, P.: Estimated stocks of circumpolar permafrost carbon with quantified uncertainty ranges and identified data gaps. Biogeosciences 11, 6573–6593 (2014)
Turner, J., Overland, J.E., Walsh, J.E.: An arctic and antarctic perspective on recent climate change. Int. J. Climatol. 27, 277–293 (2007)
Hansen, J., Ruedy, R., Glascoe, J., Sato, M.: Giss analysis of surface temperature change. J. Geophys. Res. Atmosph. 104, 30997–31022 (1999)
Assessment, A.C.I.: Impacts of a Warming Arctic-Arctic Climate Impact Assessment, by Arctic Climate Impact Assessment, vol. 1, p 144. Cambridge University Press, Cambridge, UK (2004). ISBN 0521617782
Koven, C.D., Ringeval, B., Friedlingstein, P., Ciais, P., Cadule, P., Khvorostyanov, D., Krinner, G., Tarnocai, C.: Permafrost carbon-climate feedbacks accelerate global warming. Proc. Nat. Acad. Sci. 108, 14769–14774 (2011)
Osterkamp, T.: Response of Alaskan permafrost to climate. In: Fourth International Conference on Permafrost, Fairbanks, Alaska, pp 17–22 (1983)
Walvoord, M.A., Striegl, R.G.: Increased groundwater to stream discharge from permafrost thawing in the Yukon River Basin: potential impacts on lateral export of carbon and nitrogen. Geophysical Research Letters, pp. 34 (2007)
Lyon, S., Destouni, G., Giesler, R., Humborg, C., Mörth, C.-M. , Seibert, J. , Karlsson, J., Troch, P.: Estimation of permafrost thawing rates in a sub-arctic catchment using recession flow analysis. Hydrol. Earth Syst. Sci. 13, 595–604 (2009)
Pachauri, R.K., Allen, M., Barros, V., Broome, J., Cramer, W., Christ, R., Church, J., Clarke, L., Dahe, Q., Dasgupta, P., et al.: Climate change 2014: synthesis report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (2014)
Koven, C.D., Riley, W.J., Stern, A.: Analysis of permafrost thermal dynamics and response to climate change in the CMIP5 Earth System Models. J. Clim. 26, 1877–1900 (2013)
Painter, S., Moulton, J., Wilson, C.: Modeling challenges for predicting hydrologic response to degrading permafrost. Hydrogeology Journal, pp. 1–4
Kurylyk, B.L., MacQuarrie, K.T., McKenzie, J.M.: Climate change impacts on groundwater and soil temperatures in cold and temperate regions: implications, mathematical theory, and emerging simulation tools. Earth-Sci. Rev. 138, 313–334 (2014)
Harlan, R.: Analysis of coupled heat-fluid transport in partially frozen soil. Water Resour. Res. 9, 1314–1323 (1973)
Guymon, G.L., Luthin, J.N.: A coupled heat and moisture transport model for arctic soils. Water Resour. Res. 10, 995–1001 (1974)
Taylor, G.S., Luthin, J.N.: A model for coupled heat and moisture transfer during soil freezing. Can. Geotechn. J. 15, 548–555 (1978)
Takata, K., Emori, S., Watanabe, T.: Development of the minimal advanced treatments of surface interaction and runoff. Glob. Planet. Chang. 38, 209–222 (2003)
Nicolsky, D., Romanovsky, V., Alexeev, V., Lawrence, D.: Improved modeling of permafrost dynamics in a GCM land-surface scheme. Geophysical research letters, pp. 34 (2007)
Lawrence, D.M., Slater, A.G., Swenson, S.C.: Simulation of present-day and future permafrost and seasonally frozen ground conditions in CCSM4. J. Clim. 25, 2207–2225 (2012)
McKenzie, J.M., Voss, C.I., Siegel, D.I.: Groundwater flow with energy transport and water–ice phase change: numerical simulations, benchmarks, and application to freezing in peat bogs. Adv. water Resour. 30, 966–983 (2007)
Bense, V., Ferguson, G., Kooi, H.: Evolution of shallow groundwater flow systems in areas of degrading permafrost, Geophysical Research Letters, pp. 36 (2009)
Painter, S.L., Karra, S.: Constitutive model for unfrozen water content in subfreezing unsaturated soils, Vadose Zone Journal, pp. 13 (2014)
Painter, S.L.: Three-phase numerical model of water migration in partially frozen geological media: model formulation, validation, and applications. Comput. Geosci. 15, 69–85 (2011)
Grimm, R.E., Painter, S.L.: On the secular evolution of groundwater on Mars. Geophys. Res. Lett. 36, n/a–n/a (2009). L24803
Frampton, A., Painter, S., Lyon, S.W., Destouni, G.: Non-isothermal, three-phase simulations of near-surface flows in a model permafrost system under seasonal variability and climate change. J. Hydrol. 403, 352 – 359 (2011)
Karra, S., Painter, S., Lichtner, P.: Three-phase numerical model for subsurface hydrology in permafrost-affected regions. Cryosphere Discuss 8, 149–185 (2014)
Lichtner, P.C., Hammond, G.E., Lu, C., Karra, S., Bisht, G., Andre, B., Mills, R.T., Kumar, J.: PFLOTRAN Web page. http://www.pflotran.org (2013)
Kumar, J., Collier, N., Bisht, G., Mills, R.T., Thornton, P.E., Iversen, C.M., Romanovsky, V.: Modeling the spatiotemporal variability in subsurface thermal regimes across a low-relief polygonal tundra landscape. Cryosphere 10, 2241–2274 (2016)
Painter, S.L., Coon, E.T., Atchley, A.L., Berndt, M., Garimella, R., Moulton, J.D., Svyatskiy, D., Wilson, C.J.: Integrated surface/subsurface permafrost thermal hydrology: model formulation and proof-of-concept simulations. Water Resour. Res. 52, 6062–6077 (2016)
Coon, E.T., Moulton, J.D., Painter, S.L.: Managing complexity in simulations of land surface and near-surface processes. Environ. Modell. Softw. 78, 134–149 (2016)
Dall’Amico, M., Endrizzi, S., Gruber, S., Rigon, R.: A robust and energy-conserving model of freezing variably-saturated soil. Cryosphere 5, 469–484 (2011)
Pikul, M.F., Street, R.L., Remson, I.: A numerical model based on coupled one-dimensional Richards and Boussinesq equations. Water Resour. Res. 10, 295–302 (1974)
Zhu, Y., Zha, Y., Tong, J., Yang, J.: Method of coupling 1-D unsaturated flow with 3-D saturated flow on large scale. Water Sci. Eng. 4, 357–373 (2011)
Hazenberg, P., Fang, Y., Broxton, P., Gochis, D., Niu, G.-Y. , Pelletier, J.D., Troch, P.A., Zeng, X.: A hybrid-3D hillslope hydrological model for use in earth system models. Water Resour. Res. 51, 8218–8239 (2015)
Coon, E.T.: ATS: The Advanced Terrestrial Simulator. http://github.com/amanzi/ats (2016)
Moulton, J.D., Berndt, M., Garimella, R., Prichett-Sheats, L., Hammond, G., Day, M., Meza, J.: High-level design of Amanzi, the multi-process high performance computing simulator, Office of Environmental Management, United States Department of Energy, Washington DC (2012)
Heroux, M., Bartlett, R., Hoekstra, V.H., Hu, J., Kolda, T., Lehoucq, R., Long, K., Pawlowski, R., Phipps, E., Salinger, A., Thornquist, H., Tuminaro, R., Wil-lenbring, J., Williams, A.: An overview of trilinos. Technical report sand2003-2927, Sandia National Laboratory (2003)
Garimella, R.V., Perkins, W.A., Buksas, M.W., Berndt, M., Lipnikov, K., Coon, E., Moulton, J.D., Painter, S.L.: Mesh infrastructure for coupled multiprocess geophysical simulations. Procedia Engineering 82, 34 – 45 (2014)
Da Veiga, L.B., Lipnikov, K., Manzini, G.: The mimetic finite difference method for elliptic problems, vol. 11, Springer (2014)
Lipnikov, K., Manzini, G., Shashkov, M.: Mimetic finite difference method. J. Comput. Phys. 257, 1163–1227 (2014)
Calef, M.T., Fichtl, E.D., Warsa, J.S., Berndt, M., Carlson, N.N.: Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem. J. Comput. Phys. 238, 188–209 (2013)
Carlson, N.N., Miller, K.: Design and application of a gradient-weighted moving finite element code I: in one dimension. SIAM J. Sci. Comput. 19, 728–765 (1998)
Atchley, A.L., Painter, S.L., Harp, D.R., Coon, E.T., Wilson, C.J., Liljedahl, A.K., Romanovsky, V.E.: Using field observations to inform thermal hydrology models of permafrost dynamics with ATS (v0.83). Geosci. Model Develop. 8, 2701–2722 (2015)
Atchley, A.L., Coon, E.T., Painter, S.L., Harp, D.R., Wilson, C.J.: Influences and interactions of inundation, peat, and snow on active layer thickness. Geophys. Res. Lett. 43, 5116–5123 (2016). 2016GL068550
Lawrence Livermore National Laboratory, A mesh and field I/O library and scientific database. https://wci.llnl.gov/simulation/computer-codes/silo (2016)
Jorgenson, M.T., Shur, Y.L., Pullman, E.R.: Abrupt increase in permafrost degradation in Arctic Alaska, Geophysical Research Letters, pp. 33 (2006)
Liljedahl, A., Hinzman, L., Schulla, J.: Ice-wedge polygon type controls low-gradient watershed-scale hydrology. In: Proceedings of the Tenth International Conference on Permafrost, vol. 1, pp 231–236 (2012)
Hinzman, L.D., Bettez, N.D., Bolton, W.R., Chapin, F.S., Dyurgerov, M.B., Fastie, C.L. , Griffith, B., Hollister, R.D., Hope, A., Huntington, H.P., et al.: Evidence and implications of recent climate change in Northern Alaska and other Arctic regions. Clim. Chang. 72, 251–298 (2005)
Rowland, J.C., Jones, C.E., Altmannm, G., Bryan, R., Crosby, B.T., Hinzman, L.D., Kane, D.L., Lawrence, D.M., Mancino, A., Marsh, P., McNamara, J.P., Romanvosky, V.E., Toniolo, H., Travis, B.J., Trochim, E., Wilson, C.J., Geernaert, G.L.: Arctic landscapes in transition: responses to thawing permafrost. Eos, Trans. Amer. Geophys Union 91, 229–230 (2010)
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Jan, A., Coon, E.T., Painter, S.L. et al. An intermediate-scale model for thermal hydrology in low-relief permafrost-affected landscapes. Comput Geosci 22, 163–177 (2018). https://doi.org/10.1007/s10596-017-9679-3
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DOI: https://doi.org/10.1007/s10596-017-9679-3