Skip to main content

Advertisement

Springer Nature Link
Log in

A coupled model for liquid water, water vapor and heat transport of saturated–unsaturated soil in cold regions: model formulation and verification

  • Original Article
  • Published:
Environmental Earth Sciences Aims and scope Submit manuscript

Abstract

In cold and arid regions, vapor movement and water flow are crucial to thermal-moisture dynamics of the active layer and control the soil microbial activity, plant growth and engineering applications. Although it is widely recognized that both liquid and water vapor movement are fundamental factors in the quantification of soil mass and energy balance, their computation is still rarely considered in most models or practical applications. Moreover, previous studies on the movement of moisture migration in unsaturated frozen soil are limited. This study was conducted to: (a) implement a fully coupled numerical model that includes water migration in both the vapor and liquid phases and heat transfer by means of conduction, convection, latent heat of vapor diffusion and phase change effects. (b) Verify the numerical model with detailed field monitoring data. (c) Analyze the role of water flow and vapor diffusion in the heat and mass transport. The result showed that the numerical model was able to fully calculate the coupled soil mass and energy budget. Thermal conduction dominated the heat transport in the deeper layer (below 75 cm) in permafrost regions, while the impact of water movement on heat in summer was significant in shallow ground. Soil water was transported by both liquid water and water vapor and water vapor contributed more than 15 % of the water flux at all depths. Vapor and liquid water transport play an important role in soil mass and energy transfer, especially for the shallow surface. It is necessary to consider the coupled liquid water, water vapor, and heat transport in predictions of soil water and heat dynamics in permafrost regions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Adriaan A, Van DG, Owe M (1994) Bare soil surface resistance to evaporation by vapor diffusion under semiarid conditions. Water Resour Res 30(2):181–188

    Article  Google Scholar 

  • Andersland OB, Ladanyi B (1994) An introduction to frozen ground engineering. Chapman and Hall, New York

    Book  Google Scholar 

  • Atchley AL, Painter SL, Harp DR et al (2015) Using field observations to inform thermal hydrology models of permafrost dynamics with ATS (v0.83). Geosci Model Dev 8:2701–2722. doi:10.5194/gmd-8-2701-2015

    Article  Google Scholar 

  • Banimahd SA, Zand-Parsa Sh (2013) Simulation of evaporation, coupled liquid water, water vapor and heat transport through the soil medium. Agric Water Manag 130:168–177

    Article  Google Scholar 

  • Biermans M, Dijkema KM, de Vries DA (1978) Water movement in porous media towards an ice front. J Hydrol 37(1):137–148

    Article  Google Scholar 

  • Campbell GS (1985) Soil physics with BASIC: transport models for soil-plant systems. Elsevier, New York

    Google Scholar 

  • Cass AG, Campbell GS, Jones TL (1981) Hydraulic and thermal properties of soil samples from the buried waster test facility. PNL-4015, Pacific Northwest Laboratory, Richland

  • Cass AG, Campbell GS, Jones TL (1984) Enhancement of thermal water vapor diffusion in soil. Soil Sci Soc Am J 48(1):25–32

    Article  Google Scholar 

  • Cheng GD (1983) The mechanism of repeated-segregation of the formation of thick layered ground ice. Cold Reg Sci Technol 8(1):57–66

    Article  Google Scholar 

  • Dall'Amico M, Endrizzi S, Gruber S et al (2011) A robust and energy-conserving model of freezing variably-saturated soil. Cryosphere 5(2):469–484

    Article  Google Scholar 

  • de Vries DA (1958) Simultaneous transfer of heat and moisture in porous media. Trans Am Geophys Union 39(5):909–916

    Article  Google Scholar 

  • Endrizzi S, Gruber S, Dall'Amico M et al (2014) GEOtop 2.0: simulating the combined energy and water balance at and below the land surface accounting for soil freezing, snow cover and terrain effects. Geosci Model Dev 7:2831–2857. doi:10.5194/gmd-7-2831-2014

    Article  Google Scholar 

  • Frampton A, Painter S, Steve WL et al (2011) Non-isothermal, three-phase simulations of near-surface flows in a model permafrost system under seasonal variability and climate change. J Hydrol 403(3–4):352–359

    Article  Google Scholar 

  • Gilpin RR (1980) A model for the prediction of ice lensing and frost heave in soils. Water Resour Res 16(6):918–930

    Article  Google Scholar 

  • Hansson K, Simunek J, Mizoguchi M et al (2004) Water flow and heat transport in frozen soil: numerical solution and freeze-thaw applications. Vadose Zone J 3(2):693–704

    Google Scholar 

  • Harlan RL (1973) Analysis of coupled heat-fluid transport in partially frozen soil. Water Resour Res 9(5):1314–1323

    Article  Google Scholar 

  • Henry GHR, Harper KA, Chen WJ et al (2012) Effects of observed and experimental climate change on terrestrial ecosystems in northern Canada: results from the Canadian IPY program. Clim Chang 115(1):207–234

    Article  Google Scholar 

  • Jassal RS, Novak MD, Black MD (2003) Effect of surface layer thickness on simultaneous transport of heat and water in a bare soil and its implications for land surface schemes. Atmos Ocean 41:259–272

    Article  Google Scholar 

  • Jiang YY, Zhuang QL, O’Donnell JA et al (2012) Modeling thermal dynamics of active layer soils and near-surface permafrost using a fully coupled water and heat transport model. J Geophys Res 113:D11110. doi:10.1029/2012JD017512

    Google Scholar 

  • Jin HJ, Chang XL, Wang SL (2007) Evolution of permafrost on the Qinghai-Xizang (Tibet) Plateau since the end of the late Pleistocene. J Geophy Res 112:F02S09. doi:10.1029/2006JF000521

    Article  Google Scholar 

  • Kane DL, Hinzman LD, Zarling JP (1991) Thermal response of the active layer to climate warming in a permafrost environment. Cold Reg Sci Technol 19:111–122

    Article  Google Scholar 

  • Karra S, Painter S, Lichtner P (2014) Three-phase numerical model for subsurface hydrology in permafrost-affected regions (PFLOTRAN-ICE v1. 0). Cryosphere 8(5):1935–1950

    Article  Google Scholar 

  • Konrad JM, Morgenstern NR (1980) A mechanistic theory of ice lens formation in fine-grained soil. Can Geotech J 17(5):473–486

    Article  Google Scholar 

  • Konrad JM, Morgenstern NR (1984) Frost heave prediction of chilled pipelines buried in unfrozen soils. Can Geotech J 21:100–115

    Article  Google Scholar 

  • Koopmans RWR, Miller RD (1966) Soil freezing and soil water characteristic curves. Soil Sci Soc Am J 30(6):680–685

    Article  Google Scholar 

  • Kroener E, Vallati A, Bittelli M (2014) Numerical simulation of coupled heat, liquid water and water vapor in soils for heat dissipation of underground electrical power cables. Appl Therm Eng 70:510–523

    Article  Google Scholar 

  • Li SX, Cheng GD (1996) The future thermal regime of numerical simulating permafrost on Qinghai-Xizang (Tibet) Plateau, China, under climate warming. Sci China (Series D) 39(4):434–441

    Google Scholar 

  • Li SY, Lai YM, Pei WS et al (2014) Moisture-temperature changes and freeze-thaw hazards on a canal in seasonally frozen regions. Nat Hazards 72:287–308

    Article  Google Scholar 

  • Ling F, Wu QB, Zhang TJ, et al (2012) Modelling Open-Talik Formation and Permafrost Lateral Thaw under a Thermokarst Lake, Beiluhe Basin, Qinghai-Tibet Plateau. Permafr Periglac Processes 23(4):312–321

    Article  Google Scholar 

  • Ma W, Zhang LH, Yang CS (2015) Discussion of the applicability of the generalized Clausius-Clapeyron equation and the frozen fringe process. Earths-Sci Rev 142:47–59

    Article  Google Scholar 

  • Mao XS, Li N, Wang BG et al (2006) Coupling model and numerical simulation of moisture-heat-stress fields in permafrost embankment. J Changan Univer (Nat Sci Edit) 26(4):16–19

    Google Scholar 

  • McKenzie JM, Voss CI, Siegel DI (2007) 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

    Article  Google Scholar 

  • Miller RD (1972) Freezing and heaving of saturated and unsaturated soils. Highway Res Rec 393:1–11

    Google Scholar 

  • Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res 12(3):513–522

    Article  Google Scholar 

  • Nelson FE, Anisimov OA, Shiklomanov NI (2001) Subsidence risk from thawing permafrost. Nature 410:889–890

    Article  Google Scholar 

  • Niu FJ, Zhang JM, Zhang Z (2002) Engineering geological characteristics and evaluations of permafrost in Beiluhe testing field of Qinghai-Tibetan Railway. J Glaciol Geocryol 24(3):264–269

    Google Scholar 

  • O’Neill K, Miller RD (1985) Exploration of a rigid ice model of frost heave. Water Resour Res 21(4):281–296

    Article  Google Scholar 

  • Painter SL (2011) Three-phase numerical model of water migration in partially frozen geological media: model formulation, validation, and applications. Comput Geosci 15(1):69–85

    Article  Google Scholar 

  • Painter SL, Karra S (2014) Constitutive model for unfrozen water content in subfreezing unsaturated soils. Vadose Zone J. doi:10.2136/vzj2013.04.0071

    Google Scholar 

  • Pei WS, Yu WB, Li SY et al (2013) A new method to model the thermal conductivity of soil-rock media in cold regions: an example from permafrost regions tunnel. Cold Reg Sci Technol 95:11–18

    Article  Google Scholar 

  • Peppin SSL, Style RW (2013) The physics of frost heave and ice-lens growth. Vadose Zone J. doi:10.2136/vzj2012.0049

    Google Scholar 

  • Peters-Lidard CD, Blackburn E, Liang X et al (1998) The Effect of Soil Thermal Conductivity Parameterization on Surface Energy Fluxes and Temperatures. J Atmos Sci 55(7):1209–1224

    Article  Google Scholar 

  • Philip JR, de Vries DA (1957) Moisture movement in porous materials under temperature gradients. Trans Am Geophys Union 38:222–231

    Article  Google Scholar 

  • Saito H, Simunek J, Mohanty BP (2006) Numerical analysis of coupled water, vapor, and heat transport in the vadose zone. Vadose Zone J 5(2):784–800

    Article  Google Scholar 

  • Spaans EJ, Baker JM (1996) The soil freezing characteristic: its measurement and similarity to the soil moisture characteristic. Soil Sci Soc Am J 60(1):13–19

    Article  Google Scholar 

  • Tan XJ (2010) Study on the mechanism of frost heave of tunnel in cold region with high altitude and related insulation technology. Ph.D. thesis, Chinese Academy of Sciences

  • Tan XJ, Chen WZ, Yang DS et al (2014) Study on the influence of airflow on the temperature of the surrounding rock in a cold region tunnel and its application to insulation layer design. Appl Therm Eng 67:320–334

    Article  Google Scholar 

  • Timlin DJ, Pachepsky Y, Acock BA et al (2002) Error analysis of soil temperature simulations using measured and estimated hourly weather data with 2DSOIL. Agric Syst 72(3):215–239

    Article  Google Scholar 

  • van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Am J 44(5):892–898

    Article  Google Scholar 

  • Watanabe K, Wake T (2008) Capillary bundle model of hydraulic conductivity for frozen soil. Water Resour Res 44:1927–1932

    Google Scholar 

  • Wen Z, Zhang TJ, Sheng Y et al (2011) Managing ice-rich permafrost exposed of Qinghai-Tibetan railway: experiences and implementation. Eng Geol 122:316–327

    Article  Google Scholar 

  • Wen Z, Ma W, Feng WJ et al (2012) Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetan silty clay. Environ Earth Sci 66(5):1467–1476

    Article  Google Scholar 

  • Wen Z, Niu FJ, Yu QH et al (2014) The role of rainfall in the thermal-moisture dynamics of the active layer at Beiluhe of Qinghai-Tibetan plateau. Environ Earth Sci 71(3):1195–1204

    Article  Google Scholar 

  • Wen Z, Zhang ML, Ma W et al (2015) Thermal-moisture dynamics of embankments with asphalt pavement in permafrost regions of central Tibetan Plateau. Eur J Environ Civil Eng 19(4):387–399

    Article  Google Scholar 

  • Wu QB, Zhang TJ (2008) Recent permafrost warming on the Qinghai-Tibetan Plateau. J Geophys Res 113:D13108. doi:10.1029/2007JD009539

    Article  Google Scholar 

  • Wu ZW, Cheng GD, Zhu LN et al (1988) Roadbed engineering in permafrost region. Lanzhou University Press, Lanzhou

    Google Scholar 

  • Wu DY, Lai YM, Zhang MY (2015a) Heat and mass transfer effects of ice growth mechanisms in a fully saturated soil. Int J Heat Mass Transf 86:699–709

    Article  Google Scholar 

  • Wu QB, Hou YD, Yun HB et al (2015b) Changes in active-layer thickness and near-surface permafrost between 2002 and 2012 in alpine ecosystems, Qinghai-Xizang (Tibet) Plateau, China. Glob Planet Chang 124:149–155

    Article  Google Scholar 

  • Wuest SB (2007) Vapor is the principal source of water imbibed by seeds in unsaturated soils. Seed Sci Res 17(1):3–9

    Article  Google Scholar 

  • Wuest SB, Albrecht SL, Skirvin KW (1999) Vapor transport vs seed-soil contact in wheat germination. Agron J 91:783–787

    Article  Google Scholar 

  • Xu XZ, Wang JC, Zhang LX (2010) Frozen Soil Physics. Science Press, Beijing

    Google Scholar 

  • Yi SH, Wischnewski K, Langer M et al (2013) Modeling different freeze/thaw processes in heterogeneous landscapes of the Arctic polygonal tundra using an ecosystem model. Geosci Model Dev Discuss 6(3):4883–4932

    Article  Google Scholar 

  • Zeng YJ (2012) Coupled dynamics in soil: experimental and numerical studies of energy, momentum and mass transfer. New York Dordrecht London, Springer. doi:10.1007/978-3-642-34073-4

    Google Scholar 

  • Zeng YJ, Su ZB, Wan L et al (2009) Diurnal soil water dynamics in the shallow vadose zone (field site of China University of Geosciences, China). Environ Geol 58(1):11–23

    Article  Google Scholar 

  • Zeng YJ, Su ZB, Wan L et al (2011) A simulation analysis of the advective effect on evaporation using a two-phase heat and mass flow model. Water Resour Res 47:W10529. doi:10.1029/2011WR010701

    Google Scholar 

  • Zhao LT, Gray DM, Male DH (1997) Numerical analysis of simultaneous heat and mass transfer during infiltration into frozen ground. J Hydrol 200:345–363

    Article  Google Scholar 

  • Zhao L, Wu QB, Marchenko SS, Sharkhuu N (2010) Thermal state of permafrost and active layer in central Asia during the international polar year. Permafrost Periglac Process 21:198–207

    Article  Google Scholar 

  • Zhou YW, Guo DX, Qiu GQ et al (2000) Geocryology in China. Science Press, Beijing

    Google Scholar 

  • Zhu LN (1988) Study of the adherent layer on different types of ground in permafrost regions on the Qinghai-Xizang Plateau. J Glaciol Geocryol 10(1):8–14

    Google Scholar 

  • Zhu ZR, Li Y, Xue CX et al (2011) Changing tendency of precipitation in permafrost regions along Qinghai-Tibet Railway during last thirty years. J Glaciol Geocryol 33(4):846–850

    Google Scholar 

Download references

Acknowledgments

This research project was supported by the Natural Science Foundation of China (Grant No. 41471061), the National Key Basic Research Program of China (Grant No. 2012CB026101), the Research Project of the State Key Laboratory of Frozen Soils Engineering (SKLFSE-ZY-12) and the Fund of the Cold and Arid Regions Environmental and Engineering Research Institute (Grant No. HHS-TSS-STS-1502).

Author information

Authors and Affiliations

  1. State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental Engineering Research Institute, CAS, 730000, Lanzhou Gansu, China

    Mingli Zhang, Zhi Wen, Ke Xue, Liangzhi Chen & Desheng Li

  2. University of Chinese Academy of Sciences, 100049, Beijing, China

    Mingli Zhang, Ke Xue, Liangzhi Chen & Desheng Li

Authors
  1. Mingli Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ke Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Liangzhi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Desheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi Wen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, M., Wen, Z., Xue, K. et al. A coupled model for liquid water, water vapor and heat transport of saturated–unsaturated soil in cold regions: model formulation and verification. Environ Earth Sci 75, 701 (2016). https://doi.org/10.1007/s12665-016-5499-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12665-016-5499-3

Keywords