research_article September 11, 2026

Accuracy of Numerical Models in Representing Moisture Distribution for Permeable Irrigation Systems: A Comparative Evaluation Between Constant and Variable Boundary Conditions

Hawraa Yousief Abd, Faiz Hussein Al-Merib
Volume1
Issue3
Pages151-166
DOI10.5281/zenodo.22722588
Abstract

Water scarcity is one of the most prominent agricultural challenges, prompting the development of subsurface permeable-column irrigation PCI technology to rationalize water use. This study aimed to evaluate the accuracy of the HYDRUS-2D model in simulating moisture distribution in silty clay soil using a permeable column irrigation (PCI) system. Experimental and numerical investigations were carried out under constant head (CH) and variable head (VH) boundary conditions. Measured and simulated soil moisture contents were compared. Model performance was evaluated using, RMSE, MAE, R², NSE and a Paired t-test. The results showed excellent agreement between the measured and simulated values ​​under both conditions. The RMSE values ​​ranged between 0.0000 and 0.0338, the MAE values ​​ranged from 0.00015 to 0.01081, while the R² values ​​up to 0.996 and the NSE up to 0.999, which indicates excellent model performance. The constant head (CH) produced a larger extension of the wet front due to the persistence of the hydraulic head, while the (VH) provided a more realistic representation of moisture distribution, making it better suited for simulating actual field conditions. Sensitivity analysis indicated that the parameter n had the greatest influence on simulated soil moisture whereas Ks had the least effect. The Paired t-test confirmed the absence of significant differences under the (VH) (P > 0.05), and the presence of significant differences (p <0.05) under the CH between the measured and simulated values. Overall, the variable head boundary condition provided more realistic representation of field conditions and is recommended for use in the design of subsurface irrigation systems.

Keywords
Constant HeadHydrus 2DPermeable Columnunsaturated zoneVariable HeadVan Genuchtensubsurface irrigationwetting zone.
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References
  1. Abioye, E. A., Abidin, M. S. Z., Mahmud, M. S. A., Buyamin, S., Ishak, M. H. I., Rahman, M. K. I. A., Otuoze, A. O., Onotu, P., & Ramli, M. S. A. (2020). A review on monitoring and advanced control strategies for precision irrigation. Computers and Electronics in Agriculture, 173, 105441. https://doi.org/10.1016/j.compag.2020.105441
  2. Arif, C., Saptomo, S. K., Setiawan, B. I., Taufik, M., Suwarno, W. B., Nugroho, B. D. A., & Mizoguchi, M. (2024). Water saving rice cultivation using sheet-pipe subsurface irrigation. Heliyon, 10(10), e30799. https://doi.org/10.1016/j.heliyon.2024.e30799
  3. Cai, Y., Wu, P., Zhu, D., Zhang, L., Zhao, X., Gao, X., Ge, M., Song, X., Wu, Y., & Dai, Z. (2021). Subsurface irrigation with ceramic emitters: An effective method to improve apple yield and irrigation water use efficiency in the semiarid Loess Plateau. Agriculture, Ecosystems & Environment, 313, 107404. https://doi.org/10.1016/j.agee.2021.107404
  4. Dirwai, T. L., Senzanje, A., & Mabhaudhi, T. (2025). Two-dimensional modeling of nitrate transport in canola field under Moistube irrigation using HYDRUS 2D/3D. Frontiers in Sustainable Food Systems, 9, 1538750. https://doi.org/10.3389/fsufs.2025.1538750
  5. Fan, Y., Ma, L., Wei, H., & Zhu, P. (2021). Numerical investigation of wetting front migration and soil water distribution under vertical line source irrigation with different influencing factors. Water Supply, 21(5), 2233–2248. https://doi.org/10.2166/ws.2021.054
  6. Fan, Y., Yang, Z., & Wei, H. (2021). Establishment and verification of the prediction model of soil wetting pattern size in vertical moistube irrigation. Water Supply, 21(1), 331–343. https://doi.org/10.2166/ws.2020.326
  7. Gardner, W. R., Hillel, D., & Benyamini, Y. (1970). Post‐Irrigation Movement of Soil Water: 2. Simultaneous Redistribution and Evaporation. Water Resources Research, 6(4), 1148–1153. https://doi.org/10.1029/WR006i004p01148
  8. Ghorbani, A., Sadeghi, M., Tuller, M., Durner, W., & Jones, S. B. (2024). A generalized van Genuchten model for unsaturated soil hydraulic conductivity. Vadose Zone Journal, 23(5), e20369. https://doi.org/10.1002/vzj2.20369
  9. HILLEL, D. (1998). Redistribution of water in soil. Environmental Soil Physics, 449–470.
  10. Jafari, Z., Matinkhah, S., & Mosaddeghi, M. R. (2022). Wetting patterns in a subsurface irrigation system by using reservoirs of different permeabilities: Experimental and HYDRUS-2D/3D modeling. In Review. https://doi.org/10.21203/rs.3.rs-1201561/v1
  11. Javadi, A., & Askari, K. O. A. (2024). Impact of alteration in soil hydraulic variables on collective infiltration using HYDRUS-1D. International Journal of Water, 16(2), 142–158. https://doi.org/10.1504/IJW.2024.143305
  12. Jinhong, S., Xinlin, H., Yanwei, F., Chunxia, W., Shuhan, C., & 1. College of Water Conservancy&Architectural Engineering, Shihezi University, Shihezi 832000, Xinjiang, China 2. Key Laboratory of Cold and Arid Regions Eco-Hydraulic Engineering of Xinjiang Production&Construction Corps, Shihezi University, Shihezi 832000, Xinjiang, China 3. National Center for Efficient Irrigation Engineering and Technology Research, Shihezi University, Shihezi 832000, Xinjiang, China 4. School of Civil and Hydraulic Engineering, Lanzhou University of Technology, Lanzhou 730050, China. (2025). Numerical simulation and experimental validation of soil moisture infiltration patterns under underground porous membranes: International Journal of Agricultural and Biological Engineering, 18(6), 144–157. https://doi.org/10.25165/j.ijabe.20251806.9886
  13. Juraev, F., & Karimov, G. (2020). Water saving technique and technology of subsurface irrigation. IOP Conference Series: Materials Science and Engineering, 883(1), 012095. https://doi.org/10.1088/1757-899X/883/1/012095
  14. Kandelous, M. M., & Šimůnek, J. (2010). Numerical simulations of water movement in a subsurface drip irrigation system under field and laboratory conditions using HYDRUS-2D. Agricultural Water Management, 97(7), 1070–1076. https://doi.org/10.1016/j.agwat.2010.02.012
  15. Lazarovitch et al. (2023). Modeling of irrigation and related processes with HYDRUS. In Advances in Agronomy (Vol. 181, pp. 79–181). Elsevier. https://doi.org/10.1016/bs.agron.2023.05.002
  16. Mekouar, M. A. (2023). 15. Food and Agriculture Organization of the United Nations (FAO). Yearbook of International Environmental Law, 32(1), 298–304. https://doi.org/10.1093/yiel/yvac040
  17. Phogat, V., Skewes, M. A., Mahadevan, M., & Cox, J. W. (2013). Evaluation of soil plant system response to pulsed drip irrigation of an almond tree under sustained stress conditions. Agricultural Water Management, 118, 1–11. https://doi.org/10.1016/j.agwat.2012.11.015
  18. Rasheed, Z. K. (2021). MODELING OF SUBSURFACE HORIZONTAL POROUS PIPE IRRIGATION UNDER DIFFERENT CONDITIONS. IRAQI JOURNAL OF AGRICULTURAL SCIENCES, 52(4), 949–959. https://doi.org/10.36103/ijas.v52i4.1405
  19. Rasheed, Z. K., & Abid, M. B. (2018). Numerical Modeling of Water Movement from Buried Vertical Ceramic Pipes through Soils. Journal of Engineering, 24(6), 72–85. https://doi.org/10.31026/j.eng.2018.06.06
  20. Reddy, K. R. K., & Singh, V. (2025). Subsurface flow model for estimating 2D wetting pattern in drip irrigation. CLEAN – Soil, Air, Water, 53(1), 2300236. https://doi.org/10.1002/clen.202300236
  21. Rocha, D., Abbasi, F., & Feyen, J. (2006). Sensitivity Analysis of Soil Hydraulic Properties on Subsurface Water Flow in Furrows. Journal of Irrigation and Drainage Engineering, 132(4), 418–424. https://doi.org/10.1061/(ASCE)0733-9437(2006)132:4(418)
  22. Šimůnek, J., Van Genuchten, M. Th., & Šejna, M. (2016). Recent Developments and Applications of the HYDRUS Computer Software Packages. Vadose Zone Journal, 15(7), 1–25. https://doi.org/10.2136/vzj2016.04.0033
  23. Siyal, A. A., & Skaggs, T. H. (2009). Measured and simulated soil wetting patterns under porous clay pipe sub-surface irrigation. Agricultural Water Management, 96(6), 893–904. https://doi.org/10.1016/j.agwat.2008.11.013
  24. Struthers, I., Hinz, C., & Sivapalan, M. (2006). A multiple wetting front gravitational infiltration and redistribution model for water balance applications. Water Resources Research, 42(6), 2005WR004645. https://doi.org/10.1029/2005WR004645
  25. Van Genuchten, M. Th. (1980a). A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal, 44(5), 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x
  26. Van Genuchten, M. Th. (1980b). A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal, 44(5), 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x
  27. Vishwakarma, D. K., Kumar, R., Abed, S. A., Al-Ansari, N., Kumar, A., Kushwaha, N. L., Yadav, D., Kumawat, A., Kuriqi, A., Alataway, A., Dewidar, A. Z., & Mattar, M. A. (2023). Modeling of soil moisture movement and wetting behavior under point-source trickle irrigation. Scientific Reports, 13(1), 14981. https://doi.org/10.1038/s41598-023-41435-4
  28. Wang, C., Ye, J., Zhai, Y., Kurexi, W., Xing, D., Feng, G., Zhang, Q., & Zhang, Z. (2023). Dynamics of Moistube discharge, soil-water redistribution and wetting morphology in response to regulated working pressure heads. Agricultural Water Management, 282, 108285. https://doi.org/10.1016/j.agwat.2023.108285
  29. Wang, X., Huang, Z., Qin, H., & Dai, F. (2025). Sensitivity analysis of VG model parameters for infiltration in undisturbed loess under ponding conditions using the HYDRUS-1D model. Scientific Reports, 15(1), 25204. https://doi.org/10.1038/s41598-025-11058-y
  30. Zamani, S., Fatahi, R., & Provenzano, G. (2022). A Comprehensive Model for Hydraulic Analysis and Wetting Patterns Simulation under Subsurface Drip Laterals. Water, 14(12), 1965. https://doi.org/10.3390/w14121965
  31. Zhai, Y., Kurexi, W., Wang, C., Zhu, C., Zhang, Z., & Li, Y. (2023). Modelling Soil Water Infiltration and Wetting Patterns in Variable Working-Head Moistube Irrigation. Agronomy, 13(12), 2987. https://doi.org/10.3390/agronomy13122987
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