Evaluation of Some Empirical and Semi-Empirical Equations for Soil Water Infiltration in Various Soil Texture Groups in a Semi-Arid Region

Document Type : Research Paper

Authors

• Ali Reza Vaezi ¹
• Mortaza Yavari ²
• Mohammad - Sadegh Askari ¹

¹ Department of Soil Science and Engineering, Faculty of Agriculture. University of Zanjan, Zanjan, Iran.

² Department of Soil Science and Engineering, Faculty of Agriculture, University of Zanjan, Zanjan, Iran

Abstract

Keywords

• Double-ring
• Infiltration modeling
• Infiltration rate
• Soil permeability
• Soil texture

Main Subjects

• فیزیک خاک

Background and purpose:

Water infiltration into soil, as a key process in the hydrological cycle, plays a vital role in water resources management, irrigation system design, flood prediction, and environmental conservation (Smith, 2002). Infiltration is the process by which water moves from the soil surface into the soil profile under the influence of gravitational forces (Klein & Klein, 2014). This process provides temporary water storage and facilitates its uptake by plants and soil organisms (USDOA, 2019). It is one of the best indicators of soil physical conditions and structural stability (Pinheiro, 2009). With regarding to the role of infiltration rate in surface and subsurface hydrology as well as irrigation, it has been extensively studied for more than two centuries (Milla & Kish, 2006; Ghorbani et al., 2009). In this context, modeling soil water infiltration plays a key role in water resources management, irrigation system design, and hydrological cycle prediction (Hillel, 1998). Accurate assessment of this soil physical property is essential for effective watershed management, runoff mitigation, and improved water use efficiency in agricultural lands (Vishwakarma et al., 2025). Under such conditions, a precise and comparative evaluation of infiltration models using field data from semi-arid regions of Iran is of both scientific and management significance. Therefore, the main objective of this study is to assess the accuracy of empirical models consist of Kostiakov, Kostiakov–Lewis, SCS, and Horton along with two semi-empirical models including Mishra–Singh and Sihagh, in semi-arid regions of Iran using the measured field data.

Materials and methods:

This study was conducted in Zanjan province located from 35°35′ to 37°15′ N latitude and 45°25′ to 47°15′ E longitude. To investigate water infiltration rate and the physical–chemical properties of soils, 68 sampling sites were selected through field surveys based on criteria including land use, vegetation cover, soil texture, and available soil survey maps, in order to represent the dominant variability of soils in the area Disturbed soil samples were collected from the 0–60 cm depth, and undisturbed samples were taken from the 0–20 cm depth using standard core cylinders. Disturbed samples were used to determine soil particle size distribution, electrical conductivity (EC), pH, organic matter content, and equivalent calcium carbonate, whereas undisturbed samples were used to measure bulk density in the laboratory. Particle size distribution was determined according to the USDA classification system, using dry sieving for particles larger than 0.05 mm and the hydrometer method described by Yavari et al. (2021) for finer particles (silt and clay). Based on the USDA textural classification, soils were grouped into three textural classes: coarse-textured (sandy loam and loamy sand), medium-textured (clay loam, loam, sandy clay loam and silt loam), and fine-textured soils (clay, silty clay and silty clay loam). Water infiltration experiments were carried out at each sampling site using the double-ring infiltrometer method (30 cm and 60-cm in diameters) in accordance with ASTM D3385. The infiltrated depth of water was recorded at specified time intervals until the infiltration rate approached a steady state, and the data were used to calculate cumulative infiltration, initial infiltration rate, and final infiltration rate. The measured infiltration data were fitted to four empirical models (Kostiakov, Kostiakov–Lewis, Soil Conservation Service, and Sayehag et al.) and two semi-empirical models (Horton and Mishra–Singh). Model parameters were estimated using the Solver tool in Excel by minimizing the sum of squared errors. Model performance was evaluated using the coefficient of determination (R²), root mean square error (RMSE), mean absolute deviation (MAD), and mean absolute percentage error (MAPE). Statistical analyses and graphical representations were performed using SPSS and Excell software, respectively.

Results:

The results of indicated that, across all three soil textural groups, simple empirical models—particularly the Kostiakov–Lewis and Kostiakov models appeared the most accurate, stable, and reliable performance in simulating water infiltration rate in the soils. In coarse-textured soils, the Kostiakov–Lewis model exhibited the best fit to observed data (R² = 0.999, RMSE = 0.38, MAPE = 5.07%, MAD = 0.31), while the Kostiakov model also accurately reproduced the actual infiltration trend even under conditions of high permeability and initial infiltration times (R² = 0.999, RMSE = 0.42, MAPE = 6.38%, MAD = 0.34). In contrast, more complex and semi-empirical models showed weaker performance. In medium-textured soils, the overall performance patterns of the models were similar to those in coarse-textured soils. Newertheles, the magnitude of errors slightly increased which was attributed to the greater complexity of pore distribution and structural heterogeneity in these soils. However, the Kostiakov–Lewis model still provided the most accurate estimates in these soils (R² = 0.999, RMSE = 0.46, MAPE = 6.68%, MAD = 0.38) which is associated with the role of the final infiltration rate in improving the simulation of the infiltration process. In fine-textured soils, the Kostiakov–Lewis model (R² = 0.999, RMSE = 0.23, MAPE = 3.05%, MAD = 0.17) and, subsequently, the Kostiakov model with minimal error and the higher accuracy successfully simulated the infiltration rate process and the transition from initial to steady-state condition. Despite the SCS and Sayehag models showed relatively acceptable coefficients of determination, R², exhibited the higher errors across all textural groups, particularly in fine-textured soils. This result indicates the limitations of these models for various field locations and sensitivity to assumptions and empirical coefficients. The semi-empirical models of Horton and Mishra–Singh demonstrated intermediate performance and in consequence they did not provide sufficient accuracy for quantitative prediction of infiltration.

Conclusion:

The study showed that simple empirical models, especially Kostiakov–Lewis appered the most accurate, stable, and reliable simulation of water infiltration across all soil textural groups. The Kostiakov model also performed well, even in the soils with higher permeability and at initial infiltration times. In contrast, the semi-empirical models such as Horton, SCS, and Sihagh exhibited higher errors and unstable performance due to more sensitivity of models coefficient to soil variables. The Mishra–Singh model offered intermediate performance, serving as a middle-ground option. Slightly higher errors in medium-textured soils were attributed to greater heterogeneity of soil pores. Overall, the simplicity and statistical stability of Kostiakov–Lewis make it as a practical and reliable tool for simulating infiltration process in semi-arid soils.

Funding

This study was conducted with the equipment support of the Department of Soil Science and Engineering and with the financial and moral support of the Vice Chancellor for Research of the University of Zanjan. Financial support for this research was provided by the Faculty of Agriculture, University of Zanjan, in the form of a graduate thesis grant for the first author and research grants for the co-authors.

Authorship contribution

All authors contributed substantially to the study. They participated in the design and implementation of the research, data collection, statistical analyses, interpretation of results, manuscript preparation, revision, and final approval of the manuscript. The contributions of the authors in this thesis-derived manuscript were approximately as follows:

- First Author (Graduate Student): Sample preparation, conducting experiments, data collection, performing calculations, statistical analyses, interpretation of results, and preparation of the manuscript draft.

- Second Author (Supervisor): Research design, supervision of the research process, evaluation of results, manuscript revision, and finalization of the manuscript.

- Third Author (Advisor): Research supervision, manuscript review, and revision

Declaration of Generative AI and AI-assisted technologies in the writing process

This manuscript is the result of field research and direct writing by the authors. No generative artificial intelligence or AI-assisted technologies were used at any stage of the research or manuscript preparation. The authors take full responsibility for the content of the manuscript.

Data availability statement

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Acknowledgements

The authors would like to express their sincere gratitude to the Vice Chancellor for Research of the University of Zanjan for the financial support provided for this study.

Ethical considerations

This research was approved by the Department of Soil Science and the Faculty of Agriculture Council of the University of Zanjan in accordance with the relevant regulations. The authors confirm that all ethical principles related to conducting and publishing scientific research have been fully observed.

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this manuscript