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RESEARCH PAPER
A novel statistical-physical model of soil heat capacity
1
Faculty of Civil Engineering and Environmental Sciences, Białystok University of Technology,
Wiejska 45 E, 15-351 Białystok, Poland
2
Institute of Agrophysics, Polish Academy of Sciences, Doświadczalna 4, 20-290 Lublin, Poland
These authors had equal contribution to this work
Final revision date: 2025-10-20
Acceptance date: 2025-10-24
Publication date: 2026-01-26
Corresponding author
Jerzy Lipiec
Zakład Badań Systemu Gleba-Roślina, Instytut Agrofizyki PAN, ul. Doświadczalna 4, 20-290, Lublin, Poland
Zakład Badań Systemu Gleba-Roślina, Instytut Agrofizyki PAN, ul. Doświadczalna 4, 20-290, Lublin, Poland
Int. Agrophys. 2026, 40(2): 143-157
HIGHLIGHTS
- A statistical-physical heat capacity estimation model was proposed
- The model exhibited good performance for soil aggregate beds and field soils
- The performance of the novel model was similar to that of the existing models
- The new model does not require the choice of parameters in the equations
KEYWORDS
TOPICS
ABSTRACT
The heat capacity is a key parameter affecting heat storage and transfer in soil. Therefore, in this study, we proposed a novel statistical-physical model based on concepts of specific heat, the principle of energy conservation, and configurations of mineral, organic, water, and air particles to estimate the volumetric heat capacity. The novel model does not require the choice of parameters in the equations. It was compared with measured results for soil aggregate beds and two field soils. It can be concluded that the statistical-physical model’s predictability of heat capacity was suitable for all the soil specimens. The measured and statistical-physical model-predicted volumetric heat capacities increased with the increasing water content and with the decreasing aggregate size. The good agreement between the model-predicted and measured heat capacities confirmed that the model assumptions regarding the specific heats of soil components and their averaging in the proposed model were adequately established. The proposed easy-to-use and flexible model can be applied to evaluate heat capacity in response to soil management practices and land use. The heat capacities predicted by the statistical-physical model agree well with those from the traditional analytic models proposed by de Vries (1963) and Zhao et al. (2016).
FUNDING
This work was partially funded by the HORIZON 2020, European Commission, Programme: H2020-SFS-2015-2: SoilCare for profitable and sustainable crop production in Europe, project No. 677407 (SoilCare, 2016-2021).
CONFLICT OF INTEREST
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
REFERENCES (56)
1.
Bi, J., Li, L., Liu, Z., Wu, Z., Wang, G., 2024a. Assessment and enhancement of soil freezing characteristic curve estimation models. Cold Reg. Sci. Technol. 218, 104090, https://doi.org/10.1016/j.cold....
2.
Bi, J., Pan, Y., Yang, S., Li, R., Wu, Z., 2024b. Predicting the volumetric heat capacity of freezing soils using the soil freezing characteristic curve. J. Hydrol. 645, 132151, https://doi.org/10.1016/j.jhyd....
3.
Bi, J., Pan, Y., Yang, S., Zhao, G., Wu, Z., 2024c. A thermal conductivity model for granular geomaterials with low porosity during the freezing process. Int. J. Heat Mass Transf. 233 126050, https://doi.org/10.1016/j.ijhe....
4.
Bolinder, M.A., Crotty, F., Elsen, A., Frąc, M., Kismányoky, T., Lipiec, J., et al., 2020. The effect of crop residues, cover crops, manures and nitrogen fertilization on soil organic carbon changes in agroecosystems: A synthesis of reviews. Mitig. Adapt. Strateg. Glob. Change 25, 929-952, https://doi.org/10.1007/s11027....
5.
Chun, B., Guldmann, J., 2018. Impact of greening on the urban heat island: seasonal variations and mitigation strategies. Comput. Environ. Urban Syst. 71, 165-176.
6.
Clauser, C., 2021. Thermal storage and transport properties of rocks, I: Heat Capacity and Latent Heat. Encyclopedia of Solid Earth Geophysics. In: Gupta, H.K. (Ed.) Springer International Publishing 1760-1768, https://doi.org/10.1007/978-3-....
7.
COMSOL, Comsol application library. Phase Change Models, 2023, https://www.comsol. com/model/phase-change-474 (Retrieved January 16, 2025).
8.
de Vries, D.A., 1963. Thermal properties of soils. In: van Wijk, W.R. (Ed.), Physics of Plant Environment, North-Holland Publishing Company, Amsterdam, 210-235.
9.
Dilkova, R., Jokova, M., Kerchev, G., Kercheva, M., 2002 Aggregate stability as a soil quality criterion. Options Méditerranéennes A 50, 305-312.
10.
Garbowski, T., Bar-Michalczyk, D., Charazińska, S., Beata Grabowska-Polanowska, B., Kowalczyk, A., Lochyński, P., 2023. An overview of natural soil amendments in agriculture. Soil Till. Res. 225, 105462, https://doi.org/10.1016/j.stil....
11.
Gliński, J., Lipiec, J., 2018. Soil Physical Conditions and Plant Roots 1st Edition, CRC Press, 260, First Published 1990. Reissued 2018 by CRC Press Taylor and Francis Group.
12.
Gnatowski, T., Ostrowska-Ligęza, E., Kechavarzi, C., Kurzawski, G., Szatyłowicz, J., 2022. Heat capacity of drained peat soils. Appl. Sci. 12, 1579, https://doi.org/10.3390/app120....
13.
Guidolotti, G., Zenone, T., Endreny, T., Pace, R., Ciolfi, M., Mattioni, M., et al., 2025. Impact of drought on cooling capacity and carbon sequestration in urban green area. Urban Climate 59, 102244, https://doi.org/10.1016/j.ucli....
14.
He, H., Dyck, M.F., Horton, R., Ren, T., Bristow, K.L., Lv, J., et al., 2018. Development and application of the heat pulse method for soil physical measurements. Rev. Geophys. 56, https://doi.org/10.1029/2017RG....
15.
Heitman, J.L., Basinger, J.M., Kluitenberg, G.J., Ham, J.M., Frank, J.M., Barnes, P.L., 2003. Field evaluation of the dual-probe heat-pulse method for measuring soil water content contribution. Vadose Zone J. 2(4), 552-560, https://doi.org/10.2113/2.4.55....
16.
Heitman, J.L., Horton, R., 2011. Coupled heat and water transfer in soil. In: Gliński, J., Horabik, J., Lipiec, J. (Eds), Encyclopedia of Agrophysics, Springer Dordrecht, Heidelberg, London, New York, 155-162.
17.
Huang, J., Hartemink, A.E., 2020. Soil and environmental issues in sandy soils. Earth-Science Reviews, 208, 1-22. https://doi.org/10.1016/j.ears....
18.
Jiang, S., Dong, S., Ni, L., 2025. Performance of earth to air heat exchanger under freezing soil conditions, Appl. Therm. Eng. 262, 125269, https://doi.org/10.1016/j.appl....
19.
Kekelia, B., 2012. Heat transfer to and from a reversible thermosiphon placed in porous media. Ph.D. Thesis, The University of Utah, Salt Lake City, UT, USA, https://search.proquest.com/op... (accessed on 21 September 2018).
20.
Kluitenberg, G.J., 2002. Heat capacity and specific heat. In: Dane, J.H., Topp G.C. (Eds), Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA and ASA, Madison, WI, 1201-1208.
21.
Kodešová, R., Vlasáková, M., Fér, M., Teplá, D., Jakšík, O., Neuberger, P., Adamovský, R., 2013. Thermal properties of representative soils of the Czech Republic. Soil Water Res., 8, 141-150.
22.
Lahoori, M., Jannota, Y., Rosin-Paumier, S., Boukelia, A., Masrouri, F., 2020. Measurement of the thermal properties of unsaturated compacted soil by the transfer function estimation method. Appl. Therm. Eng. 167, 114795. https://doi.org/10.1016/j.appl....
23.
Langa, S., Magwaza, L.S., Mditshwa, A., Tesfay, S.Z., 2024. Temperature effects on seed germination and seedling biochemical profile of Cannabis landraces. Int. J. Plant Biol. 15 1032-1053, https://doi.org/10.3390/ijpb15....
24.
Lei, H., Bo, Y., Ma, C., Wang, L., Zhang, W., 2023. Variation pattern and prediction model of clay specific heat capacity considering multi-factors. Rock and Soil Mechanics 44, Suppl. 1-11.
25.
Li, Q., Feng, P., Wang, R., An, N., Bai, R., Yang, G., et al., 2025. Numerical simulation of frost heave and thaw settlement characteristics in a complex pipe-soil system in the seasonally frozen ground. Appl. Sci. 15, 4628, https://doi.org/10.3390/app150....
26.
Lipiec J., Walczak R., Witkowska-Walczak B., Nosalewicz A., Słowińska-Jurkiewicz A., Sławiński C., 2007. The effect of aggregate size on water retention and pore structure of silt loam soils of different genesis. Soil Till. Res. 97, 239-246.
27.
Luo, Q., Guo, Y., Dai, A., Li, Y., Cheng, J., Wang, P., et al., 2025. Research on the evaluation model of soil heat loss in solar greenhouses. Energy 322, 135665, https://doi.org/10.1016/j.ener....
28.
Nimmo, J.R., 2004. Aggregation: Physical Aspects. In: D. Hillel (Ed.), Encyclopedia of Soils in the Environment: London, Academic Press, 1-11.
29.
Noborio, K., McInnes, K.J., Heilman, J.L., 1996. Measurements of soil water content, heat capacity, and thermal conductivity with a single TDR probe. Soil Sci. 161, 22-28.
30.
Shehata, M., Heitman, J., Sayde, C., 2022. High-resolution field measurement of soil heat capacity and changes in soil moisture using a Dual-Probe Heat-Pulse Distributed Temperature Sensing approach. Water Resour. Res. 58, e2021WR031680, https://doi.org/10.1029/2021WR....
31.
Sikora, E., 1983. Thermal properties of aggregate soil samples for different aggregate diameter and moisture, Ph.D. Thesis, Agricultural University, Lublin, Poland, 106.
32.
Sikora, E., Malicki, M., 1984. Determination of the specific heat of moist soil by a calorimetric method. Polish J. Soil Sci. 17, 1-2, 53-57.
33.
Skauge, A., Fuller, N., Hepler, L.G., 1983. Specific heats of clay minerals: Sodium and calcium kaolinites, sodium and calcium montmorillonites, illite, and attapulgite, Thermochim. Acta 61, 139-145, https://doi.org/10.1016/0040-6....
34.
Soil Survey Staff, 1975. Soil Taxonomy: A Basic System of Soil Classification for Making and Interpreting Surveys. USDA-SCS Agriculture Handbook, U.S. Gov. Print. Office, Washington, D.C.
35.
Tarnawski, V.R., Wagner, B., Leong, W.H., McCombie, M., Coppa, P., Bovesecchi, G., 2021. Soil thermal conductivity model by de Vries: Re-examination and validation analysis. Eur. J. Soil Sci. 72, 1940-1953. https://doi.org/10.1111/ejss.1....
36.
Tisdall, J.M., Oades, J.M., 1982. Organic matter and water-stable aggregates in soils, J. Soil Sci. 33, 141-163, https://doi.org/10.1111/j.1365....
37.
Tu, S., Zhang, X., Zhou, X., 2017. A revised thermal resistance and capacity model for the ground heat exchanger under freezing soil conditions and thermal performance analysis. Procedia Eng. 205, 19-26, https://doi.org/10.1016/j.proe....
38.
Usowicz, B., 2000. Statistical and physical models of mass and energy flow in a porous medium (in Polish). Acta Agrophys. 29, 3-113.
39.
Usowicz, B., Lipiec J. 2022. Spatial variability of thermal properties in relation to the application of selected soil-improving cropping systems (SICS) on sandy soil, Int. Agrophys. 36, 269-284; https://doi.org/10.31545/intag....
40.
Usowicz, B., Lipiec, J., Łukowski, M., Bis, Z., Usowicz, J., Latawiec, A.E., 2020. Impact of biochar addition on soil thermal properties: Modelling approach. Geoderma 376, 114574, https://doi.org/10.1016/j.geod....
41.
Usowicz, B., Lipiec, J., Usowicz, J.B., Marczewski, W., 2013. Effects of aggregate size on soil thermal conductivity: comparison of measured and model-predicted data. Int. J. Heat Mass Transfer 57, 536-541.
42.
Usowicz, B., Marczewski, W., Lipiec, J., Usowicz, J.B., Sokołowska, Z., Dąbkowska-Naskręt, H., et al., 2009. Water in the soil – ground and satellite measurements in studies on climate change (in Polish). Foundation for the Development of Agrophysical Sciences, Monograph, Lublin, Poland, 1-171, ISBN: 978-83-60489-14-7.
43.
Wang, Z.H., Bou-Zeid, E., 2012. A novel approach for the estimation of soil ground heat flux. Agric. For. Meteorol. 154-155, 214-221. https://doi.org/10.1016/j.agrf....
44.
Wang, H., Garg, A., Zhang, X., Xiao, Y., Mei, G., 2020. Utilization of coconut shell residual in green roof: hydraulic and thermal properties of expansive soil amended with biochar and fibre including theoretical model. Acta Geophysica 68, 1803-1819, https://doi.org/10.1007/s11600....
45.
Wang, Y.J., Lu, Y.L., Horton, R., Ren, T.S., 2019. Specific heat capacity of soil solids: influences of clay content, organic matter, and tightly bound water. Soil Sci. Soc. Am. J. 83, 1062-1066, https://doi.org/10.2136/sssaj2....
46.
Wang, Y., Zhang, Z., Guo, Z., Chen, Y., Yang, J., Peng, X., 2023. In-situ measuring and predicting dynamics of soil bulk density in a non-rigid soil as affected by tillage practices: Effects of soil subsidence and shrinkage. Soil Till. Res. 234, 105818, https://doi.org/10.1016/j.stil....
47.
Witkowska-Walczak, B., 2000. Aggregate structure of mineral soils vs. hydrophysical characteristics (model investigations) (in Polish). Acta Agrophys. 30, 1-94.
48.
WRB IUSS Working Group, 2015. World reference base for soil resources 2014, update 2015. International Soil Classification System for Naming Soils and Creating Legends for Soil Maps. World Soil Resources Reports No. 106, FAO, Rome.
49.
Xie, X., Zeng, L., Ren, T., 2025. A data assimilation-based heat pulse method for monitoring soil hydraulic and thermal parameters in root zones, Soil Till. Res. 254, 106738, https://doi.org/10.1016/j.stil....
50.
Zhang, X., Han, Z., Li, X., 2024. Accurate identification of soil thermal parameters and groundwater flow from thermal response tests. Renew. Energy 236, 121393, https://doi.org/10.1016/j.rene....
51.
Zhang, M., Lu, Y., Ren, T., Horton, R., 2020. In-situ probe spacing calibration improves the heat pulse method for measuring soil heat capacity and water content. Soil Sci. Soc. Am. J. 84, 1620-1629, https://doi.org/10.1002/saj2.2....
52.
Zhang, Q., Wang, Y., Wu, Y., Wang, Y., Du, X., Liu, Z., et al., 2013. Effects of biochar amendment on soil thermal conductivity, reflectance, and temperature. Soil Sci. Soc. Am. J. 77, 1478-1487.
53.
Zhao, J., Ren, T., Zhang, Q., Du, Z., Wang, Y., 2016. Effects of biochar amendment on soil thermal properties in the North China Plain. Soil Sci. Soc. Am. J. 80, 1157-1166.
54.
Zheng, D.H., van der Velde, R., Su, Z.B., Wang, X., Wen, J., Booij, M.J., et al., 2015. Augmentations to the Noah model physics for application to the Yellow River source area. Part II: Turbulent heat fluxes and soil heat transport. J. Hydrometeorol. 16, 2677-2694, https://doi.org/10.1175/JHM-D-....
55.
Zhou, J., Wang, X., Xu, J., Shi, Z., 2025. Heat exchange efficiency and structural stability of assembled energy shafts: a novel shallow geothermal exploitation system for coastal urban cities. Geotherm. Energy 13, 25, https://doi.org/10.1186/s40517....
56.
Zografos, A.I., Martin, W.A., Sunderland, J.E., 1987. Equations of properties as a function of temperature for seven fluids. Comput. Methods Appl. Mech. Eng. 61, 177-187.
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