Toprak sıcaklığının ısı miktarına bağlı olarak değişiminin matematiksel modellenmesi

Toprak katmanlarındaki ısı miktarının değişimi, toprağın termo-fiziksel özellikleri, toprak mikro iklimi, toprak oluşum süreçleri vb. üzerinde önemli bir etkiye sahiptir. Bu çalışmada, toprak profilindeki katmanların anlık soğuması durumunda toprağın bir boyutlu ısı iletkenlik denklemi benzerlik teorisine göre incelenmiştir. Çözüm, hata ve tamamlayıcı hata fonksiyonları kullanılarak basit bir şekilde ifade edilmiştir. Toprak katmanının soğuma sürecinde, toprak derinliği boyunca sıcaklığın zamana göre değişimi, toprak derinliği ve ısı miktarının bir fonksiyonu olarak teorik bir ifade ile gösterilmiştir. Araştırma toprağının gravimetrik ısı kapasitesi 950.404 J kg-1 °C -1 olarak saptanmıştır. Araştırma dönemlerinde toprağın hacimsel ısı kapasitesi ve ısı miktarı sırasıyla (2.324-2.654)∙106 J m-3 °C -1 ve 1.027∙106-3.227∙107 J m-2 aralığında belirlenmiştir. Isı miktarının sabit olması durumunda, toprağın 0-10 cm katmanında 10 saat boyunca kaybedilen ısı işleminden sonra toprak sıcaklığı ortalama %49.20 azalmaktadır. Toprak profilinin alt katmanlarında ise sıcaklığın azalması düşük düzeyde gerçekleşmektedir. Azalma süreci aynı zamanda toprağın gravimetrik ısı kapasitesine, hacimsel ısı kapasitesinin ve ısısal yayınım katsayısının değişimine de önemli derecede bağlı olmaktadır.

Anahtar Kelimeler:

Toprak sıcaklığı, Toprak sıcaklığı, Isı miktarı, Benzerlik teorisi, Isı kapasitesi, Toprak derinliği

Mathematical modeling of soil temperature change depending on heat amount

Change in the amount of heat in soil layers has a significant effect on thermo-physical properties of soil, soil microclimate, soil formation processes and etc. In this study, one dimensional thermal conductivity equation of soil is investigated according to similarity theory in case of instant cooling of soil layer. The solution is simply expressed using the error and complementary error functions. During the cooling process of the soil layer, the change in temperature of soil depth with respect to time is shown with a theoretical expression as a function of soil depth and heat amount. The gravimetric heat capacity of the research soil was determined as 950.404 J kg-1 °C-1. Volumetric heat capacity and heat quantity of the soil were determined in the range of 2.324∙ 106 - 2.654 ∙ 106 J m-3 °C-1 and 1.027∙106 - 3.227∙107 J m-2, respectively. The soil temperature decreases by an average of 49.20% after 10 hours of heat treatment in the 0-10 cm soil layer in case of constant heat amount. The temperature decrease in the lower layers of the soil occurs at a low level. The reduction process is also significantly dependent on the gravimetric heat capacity, volumetric heat capacity and the coefficient of thermal diffusion of the soil.

Keywords:

Soil temperature, Heat quantity, Similarity theory, Heat capacity, Soil depth,

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Afify, A.A. (2009). Similarity solution in MHD: Effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection. Commun Nonlinear Sci Numer Simulat, 14, 2202-2214.
Antonopoulos, V.Z. (2006). Water movement and heat transfer simulations in a soil under ryegrass. Biosystems Engineering, 95 (1), 127-138.
Arias-Penas, D., Castro-Garcia, M.P, Rey-Ronco, M.A, & Alonso-Sanchez, T. (2015). Determining the thermal diffusivity of the ground based on subsoiltemperatures. Preliminary results of an experimental geothermalborehole study QTHERMIE-UNIOVI. Geothermics, 54, 35-42.
Arkhangel’skaya, T.A., Guber, A.K., Mazirov, M.A., & Prokhorov, M.V. (2005). The temperature rejime of soils in Vladimir Opol’e Region. Pocvovedeniye, 7, 832-843.
Arkhangel’skaya, T.A., & Umarova, A.B. (2008). Thermal diffusivity and temperature regime of soils in large lysimeters of the experimental soil station of Moscow State University. Pocvovedeniye, 3, 311-320.
Barraza, V., Grings, F., Franco,M., Douna, V., Entekhabi, D., Restrepo-Coupe, N., Huete, A., Gassmann, M., & Roitberg, E. (2019). Estimation of latent heat flux using satellite land surface temperature and a variational data assimilation scheme over a eucalypt forest savanna in Northern Australia. Agricultural and Forest Meteorology, 268, 341–353.
Braud, I., Dantas-Antonino, A.C., Vauclin, M., Thony, J.L., & Ruelle, P. (1995). A simple soil-plant-atmosphere transfer model (SiSPAT) development and field verification. Journal of Hydrology, 166 (3-4), 213-250.
Camillo, P.J., Gurney, R.J., & Schmugge, T.J. (1983). A soil and atmospheric boundary layer model for evapotranspiration and soil moisture studies. Water Resources Research, 19 (2), 371-380.
Chen, S., Mao, J., & Han, X. (2016). Heat transfer analysis of a vertical ground heat exchanger usingnumerical simulation and multiple regression model. Energy and Buildings, 129, 81-91.
Cichota, R., Elias, E.A., & van Lier, Q.J. (2004). Testing a finite-difference model for soil heat transfer by comparing numerical and analytical solutions. Environmental Modelling & Software, 19, 495-506.
Correia, A., Vieira, G., & Ramos, M. (2012). Thermal conductivity and thermal diffusivity of cores from a 26 meter deep borehole drilled in Livingston Island, Maritime Antarctic. Geomorphology, 155(156), 7-11.
Dengiz, O, & Ekberli, İ. (2017). Bazı vertisol alt grup topraklarının fizikokimyasal ve ısısal özelliklerinin incelenmesi. Akademik Ziraat Dergisi, 6(1), 45-52.
Ding, R., Kang, S., Li, F., Zhang, Y., & Tong, L. (2013). Evapotranspiration measurement and estimation using modified Priestley-Taylor model in an irrigated maize field with mulching. Agricultural and Forest Meteorology, 168 (1), 140-148.
Ekberli, İ., & Dengiz, O. (2016). Bazı ınceptisol ve entisol alt grup topraklarının fizikokimyasal özellikleriyle ısısal yayınım katsayısı arasındaki regresyon ilişkilerin belirlenmesi. Toprak Su Dergisi, 5(2), 1-10.
Ekberli, İ., Dengiz O, Gülser C, & Özdemir N, (2016). Benzerlik teorisinin toprak sıcaklığına uygulanabilirliği. Toprak Bilimi ve Bitki Besleme Dergisi 4 (2), 63-68.
Ekberli, İ., & Gülser, C. (2014). Estımatıon of soil temperature by heat conductıvıty equatıon. Vestnik Bashkir State Agrarian University (Вестник Башкирского Государственного Аграрного Университета), 2 (30), 12-15.
Ekberli, İ., & Gülser, C. (2015). İki boyutlu ısı iletkenliği denklemine bağlı olarak toprak sıcaklığının matematiksel modellenmesi Anadolu Tarım Bilim. Dergisi, 30 (3), 287-291.
Ekberli, İ., & Gülser, C. (2016). Toprağın ısısal yayınımının fonksiyonel değişimi ve toprak sıcaklığına etkisi. Anadolu Tarım Bilimleri Dergisi, 31 (2), 294-300.
Ekberli, İ., Gülser, C., & Mamedov, A. (2015). Toprakta bir boyutlu ısı iletkenlik denkleminin incelenmesinde benzerlik teorisinin uygulanması. Süleyman Demirel Üniversitesi Ziraat Fakültesi Dergisi, 10(2), 69-79.
Ekberli, İ., Gülser, C., & Özdemir, N. (2017). Farklı toprak derinliklerindeki sıcaklığın tahmininde parabolik fonksiyonun kullanımı. Toprak Bilimi ve Bitki Besleme Dergisi, 5 (1), 34- 38.
Ekberli, İ., & Sarılar, Y. (2014). Investıgating soil temperature variabılıty and thermal diffusivity in grass cowered and shaded areas by trees. Почвоведение и Агрохимия (Soil Science and Agrochemistry, Almaty), № 4, Алматы, pp. 17-30.
Ekberli, İ., & Sarılar, Y. (2015). Toprak sıcaklığının profil boyunca sönme derinliğinin ve gecikme zamanının belirlenmesi. Ege Üniversitesi Ziraat Fakültesinin Dergisi, 52 (2), 219-225.
Eshonkulov, R., Poyda, A., Ingwersen, J., Pulatov, A., & Streck, T. (2019). Improving the energy balance closure over a winter wheat field by accounting for minor storage terms. Agricultural and Forest Meteorology, 264, 283-296.
Evett, S.R., Agam, N., Kustas, W.K., Colaizzi, P.D., & Schwartz, R.C. (2012). Soil profile method for soil thermal diffusivity, conductivity and heat flux: Comparison to soil heat flux plates. Advances in Water Resources, 50, 41-54.
Gülser, C., & Ekberli, I. (2004). A comparison of estimated and measured diurnal soil temperature through a clay soil depth. Journal of Applied Sciences, 4(3), 418-423.
Gülser, C., Ekberli, İ., & Mamedov, A. (2019). Toprak Sıcaklığının Yüzey Isı Akışına Bağlı Olarak Değişimi. Yüzüncü Yıl Üniversitesi Tarım Bilimleri Dergisi, 29(1), 1-9.
Gülser, C., Ekberli, İ., Mamedov, A., & Özdemir, N. (2018). Faz değişimine bağlı olarak ısı iletkenliği denkleminin incelenmesi ve toprak neminin ısısal yayınıma etkisi. Anadolu Tarım Bilimleri Dergisi 33 (3), 261-269.
Goldstein, R.J., Ibele, W.E., Patankar, S.V., Simon, T.W., Kuehn, T.H., Strykowski, P.J., Tamma, K.K., Heberlein, J.V.R., Davidson, J.H., Bischof, J., Kulacki, F.A., Kortshagen, U., Garrick, S., Srinivasan, V., Ghosh, K. & Mittal, R. (2010a). Heat transfer-A review of 2004 literature. International Journal of Heat and Mass Transfer, 53, 4343-4396.
Goldstein, R.J., Ibele, W.E., Patankar, S.V., Simon, T.W., Kuehn, T.H., Strykowski, P.J., Tamma, K.K., Heberlein, J.V.R., Davidson, J.H., Bischof, J., Kulacki, F.A., Kortshagen, U., Garrick, S., Srinivasan, V., Ghosh, K., & Mittal, R. (2010b). Heat transfer-A review of 2005 literature. International Journal of Heat and Mass Transfer, 53, 4397-4447.
Hanks, R.J., & Ashcroft, G.J. (1980). Applied soil physics. Soil water and temperature applications. Springer-Verlag Berlin Heidelberg, pp. 125-144.
Hilel, D. (2004). Introduction to environmental soil physics. Elsevier Academic Press, USA, pp. 215-233.
Holmes, T.R.H., Owe, M., De Jeu, R.A.M., & Kooi, H. 2008. Estimating the soil temperature profile from a single depth observation: A simple empirical heatflow solution. Water Resources Research, 44 (2), W0241, 1-11.
Hu, G., Zhao, L., Wu X., Li, R., Wu, T., Xie, C., Qiao, Y., Shi, J., Li, W., & Cheng, G. (2016). New Fourier-series-based analytical solution to the conduction–convection equation to calculate soil temperature, determine soil thermal properties, or estimate water flux. International Journal of Heat and Mass Transfer, 95, 815-823.
Huang, F., Zhan, W., Ju, W., & Wang, Z. (2014). Improved reconstruction of soil thermal field using two-depth measurements of soil temperature. Journal of Hydrology, 519, 711-719.
Ihsak, A., (2010). Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Applied Mathematics and Computation 217, 837-842.
Jia, X., Zha, T.S., Gong, J.N., Wu, B., Zhang, Y.Q., Qin, S.G., Chen, G.P., Feng, W., Kellomaki, S., & Peltola, H. (2016). Energy partitioning over a semi-arid shrubland in northern China. Hydrological Processes. 30 (6), 972-985.
Krarti, M., Lopez-Alonzo, C., Claridge, D.E., & Kreider, J.F. (1995). Analytical model to predict annual soil surface temperature variation. Journal of Solar Energy Engineering, 177, 91-99.
Kreith, F., & Black, W.Z. (1983). Bazic Heat Transfer (in Russian). Press Mir, Moscow, 512 p.
Kutikoff, S., Lin, X., Evett, S., Gowda, P., Moorhead, J., Marek, G., Colaizzi, P., Aiken, R., & Brauer. D. (2019). Heat storage and its effect on the surface energy balance closure under advective conditions. Agricultural and Forest Meteorology, 265, 56-69.
Kuznetsov, G.V., Osipov, K.Yu., Piskunov, M.V., & Volkov, R.S. (2018). Experimental research of radiative heat transfer in a water film. International Journal of Heat and Mass Transfer, 117, 1075-1082.
Lettau, H.H. (1954). Improved models of thermal diffusion in the soil. Transactions of the American Geophysical Union, 35(1), 121-132.
Liang, H., Hu, K., Qin, W., Zuo, Q., & Zhang, Y. (2017). Modelling the effect of mulching on soil heat transfer, watermovement and crop growth for ground cover rice production system. Field Crops Research, 201, 97-107.
Liu, B.C., Liu, W., & Peng, S.W. (2005). Study of heat and moisture transfer in soil with a dry surface layer. International Journal of Heat and Mass Transfer, 48, 4579-4589.
Luikov, A.V. (1967). Theory of thermal conductivity (in Russian). Vysshaya Shkola Press, Moscow, 599 p.
Luikov, A.V., & Mikhailov, YuA (1965). Theory of energy and mass transfer. Pergamon Press, Oxford, England, 392 p. Ma, J., Zha, T., Jia,X., Tian, Y., Bourque, C.P.-A., Liu, P., Bai, Y., Wu, Y., Ren, C., Yu, H., Zhang, F., Zhou, C., & Chen, W. (2018). Energy and water vapor exchange over a young plantation in northern China. Agricultural and Forest Meteorology, 263, 334-345.
Milly, P.C.D. (1986). An event‐based simulation model of moisture and energy fluxes at a bare soil surface. Water Resources Research, 22 (12), 1680-1692.
Novak, M.D., & Black, T.A. (1985). Theoretical determination of the surface energy balance and thermal regimes of bare soils. Boundary-Layer Meteorology, 33 (4), 313-333.
Okoya, S.S. (2001). Simılarity temperature profiles for some nonlinear reaction - diffusion equations. Mechanics Research Communications, 28(4), 477-484.
Oncley, S.P., Foken, T., Vogt, R., Kohsiek, W., DeBruin, H.A.R., Bernhofer, C., Christen, A., van Gorsel, E., Grantz, D., Feigenwinter, C., Lehner, I., Liebethal, C., Liu, H., Mauder, M., Pitacco, A., Ribeiro, L., & Weidinger, T. (2007). The energy balance experiment EBEX-2000. Part I: overview and energy balance. Boundary-Layer Meteorology, 123, 1-28.
Oosterkamp, A., Ytrehus, T., & Galtung, S.T. (2016). Effect of the choice of boundary conditions on modelling ambient to soil heat transfer near a buried pipeline. Applied Thermal Engineering, 100, 367-377.
Passerat de Silans, A., Bruckler, L., Thony, J.L., & Vanclin, M. (1989). Numerical modeling of coupled heat and water flows during drying in a stratified bare soil - Comparison with field observations. Journal of Hydrology, 105 (1-2), 109-138.
Passerat de Silans, A.M.B., Monteny , B.A., Lhomme, J.P. (1996). Apparent soil thermal diffusivity, a case study: HAPEX-Sahel experiment. Agricultural and Forest Meteorology, 81, 201-216.
Qi. J., Zhang, X., & Cosh, M.H. (2019). Modeling soil temperature in a temperate region: A comparison between empirical and physically based methods in SWAT. Ecological Engineering, 129, 134-143.
Russell, E.S., Liu, H., Gao, Z., Finn, D., & Lamb, B. (2015). Impacts of soil heat flux calculation methods on thesurface energy balance closure. Agricultural and Forest Meteorology, 214-215, 189-200.
Samanta, S., & Guha, A. (2012). A similarity theory for natural convection from a horizontal plate for prescribed heat flux or wall temperature. International Journal of Heat and Mass Transfer, 55, 3857-3868.
Swain, M., Swain, M., Lohmann, M., & Swain, E. (2012). Experimental determination of soil heat storage for the simulation of heat transport in a coastal wetland. Journal of Hydrology, 422-423, 53-62.
Thiery, D., Amraoui. N., & Noyer, M-L. (2018). Modelling flow and heat transfer through unsaturated chalk - Validation with experimental data from the ground surface to the aquifer. Journal of Hydrology, 556, 660–673.
Tikhonravova, P.I. (2007). Effect of the water content on the thermal diffusivity og clay loams with different degrees of salinization ih the Transvolga region. Pocvovedeniye, 1, 55-59.
Trombotto, D., & Borzotta, E. (2009). Indicators of present global warming through changes in active layerthickness, estimation of thermal diffusivity and geomorphological observations in the Morenas Coloradas rockglacier, Central Andes of Mendoza, Argentina. Cold Regions Science and Technology, 55, 321–330.
Turcotte, D.L., & Schubert, G. (1985). Geodynamics. Applications of continuum physics to geological problems (Volume 1). Mir Press, Moscow, 376 p.
van Lopik, J. H., Hartog, N., Zaadnoordijk, W.J., Cirkel, D.G., & Raoof, A. (2015). Salinization in a stratified aquifer induced by heat transfer from wel lcasings. Advances in Water Resources, 86, 32-45.
Xu, G., Li, Y., Deng, H., Li, H., & Yu, X. (2015). The application of similarity theory for heat transfer investigation in rotational internal cooling channel. International Journal of Heat and Mass Transfer, 85, 98-109.
Zhang, Y., Zhao, W., He, J., & Zhang, K. (2016). Energy exchange and evapotranspiration over irrigated seed maize agroecosystems in a desert-oasis region, northwest China. Agricultural and Forest Meteorology, 223, 48-59.
Zhu, W., Wu, B., Yan, N., Feng, X., & Xing, Q. (2014). A method to estimate diurnal surface soil heat flux from MODIS data for a sparse vegetation and bare soil. Journal of Hydrology, 511, 139-150.