Spatial variability modeling and geostatistical estimation of coefficients of some water infiltration equations in calcareous soil of Bajgah, Shiraz

Document Type : Research/Original/Regular Article

Authors

1 Former M.Sc. Student, Department of Soil Science, College of Agriculture, Shiraz University, Shiraz, Iran

2 Professor, Department of Soil Science, College of Agriculture, Shiraz University, Shiraz, Iran

3 Associate Professor, Department of Soil Science, College of Agriculture, Shiraz University, Shiraz, Iran

Abstract

Introduction
Water infiltration into soil is one of the most important soil physical processes for hydrological and agricultural applications. It plays a key role in hydrological studies, water resource management, soil conservation, irrigation systems, drainage systems, and soil erosion control in watersheds. There are various equations for determining how water infiltrates into the soil. Some of these (e.g., Philip and Green-Ampt equations) are based on the physical properties of the soil and the results of solving the relationships governing water flow in the soil. The others (e.g., Kostiakov, Kostiakov-Lewis, Horton, and US Soil Conservation Service equations) are empirical relationships obtained from analyzing the curve between infiltration rate and time without any physical background. Using these relationships avoids the waste of time and high cost required to measure infiltration in the field, especially on a large scale. The coefficients of these equations, like other soil characteristics, depend on the soil type and conditions and are subject to spatial and temporal variations. Therefore, this research aimed to study the spatial variability and model of the spatial dependence of the coefficients of different theoretical and empirical infiltration equations in the calcareous soils of Bajgah, Shiraz.
 
Materials and Methods
Infiltration tests were carried out at 50 points of the studied soil using the single-ring method. Different infiltration equations, including Horton, Kostiakov, Kostiakov-Lewis, US soil conservation service (SCS), Green-Ampt, and Philip equations were fitted to the measured data, and the coefficients of the equations were determined. Preliminary statistical checks included determining the summary statistic (measure of location, measure of spread, and shape parameters of data distribution), checking the normality of the distribution of the infiltration coefficients data, and performing necessary transformations if required. To check the spatial dependency of the data, the experimental semivariogram of the data was calculated. Various theoretical models, including spherical, exponential, and Gaussian models, were fitted and the best semivariogram model and its characteristics were determined using statistical criteria. Coefficients at unmeasured points were also estimated using the normal kriging method and the inverse distance weighting (IDW) method with different weight powers. The evaluation of the estimation methods was also carried out using the jack-knife method and the appropriate estimation method was identified. Estimation of the coefficients at points without data and zoning was done using the appropriate estimation method. The statistical and geostatistical analyses mentioned above were carried out using the software packages Excel and GS+.
 
Results and Discussion
The coefficient of variation (CV) of the studied infiltration equation coefficients varied between 12.5 and 478%, with the highest and lowest CV for the coefficients “A” of the Kostiakov-Lewis equation and “b'” of the SCS equation. The isotropic spherical model was the best-fitted model to the semivariogram of the coefficients of the Kostiakov (K and b), Horton (c, m, and a), Philip (“A”), and Kostiakov-Lewis (b') equations. Whereas, the isotropic exponential model was the best-fitted model to the coefficients of the SCS (a and b), Philip (“S”), and  Kostiakov-Lewis (K and A) equations. The range of variation (the radius of influence) of the coefficients of the infiltration equations varied from 1.96 to 211 m, respectively, for the “K” coefficient of the Kostiakov equation and the coefficients of the Kostiakov-Lewis, “a” of Horton, “S” of Philip, and “b”' of SCS equations. Among the coefficients studied, the highest and lowest nugget effect (C0) to threshold (C+C0) ratio was obtained as 0.648 and 0.5, respectively. The spatial correlation class of the infiltration equation coefficients was moderate, and the maximum and minimum radius of influence were 211 and 6.4 m, respectively, which corresponded to the “S” coefficient of Philip, the coefficients of Kostiakov-Lewis, the “a” coefficient of Horton, and the “b” coefficient of the SCS equations. The most precise and the least precise estimates were related to the “A” coefficient of Philip, “b” of Kostiakov, and “b'” of Kostiakov-Lewis equations, respectively.
 
Conclusion
In this study, spatial variations of the coefficient of various infiltration relations were investigated and modeled, and estimation and zoning were performed using the best model. Results showed that the spatial dependence class of the coefficient of infiltration relations in the study area is medium, and also, the maximum and minimum radius of influence of 211 and 6.4 m are related to the coefficient S of the Philip and the coefficients of the Kostiakov-Lewis and the coefficient a of Horton and the coefficient b of the US Soil Conservation Service equations, respectively. In other words, this study suggests geostatistical methods and limited measurements to estimate the coefficients of the infiltration equations with reasonable precision and to save time and cost when zoning or estimating these coefficients at large scales. However, due to the weak and unsuitable spatial structure, the IDW method outperformed the kriging method in some cases in the studied area and its use can lead to more precise estimates. Therefore, in cases where the spatial structure of the desired feature is weak and inappropriate, methods such as Kriging that rely on strong spatial correlation are unsuitable, and in these cases, other alternative estimation methods, such as IDW which does not depend on the presence of strong and appropriate spatial structure in the data should be used.

Keywords

Main Subjects

References

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Water and Soil Management and Modelling
Volume 4, Issue 4
2024
Pages 131-150

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  • Receive Date: 17 July 2023
  • Revise Date: 30 August 2023
  • Accept Date: 31 August 2023

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