Spatial Variability Modeling and Geostatistical Estimation of Coefficients of Some Water Infiltration Equations in a Calcareous Soil of Bajgah, Shiraz

Introduction

Infiltration is one of the most important soil physical processes in relation to hydrological and agricultural issues, which plays a key role in hydrological studies, water resource management and soil conservation, designing irrigation and drainage systems and soil erosion control in watersheds. Investigating water infiltration into the soil is mainly done using infiltration equations, and the coefficients of these equations, like other soil characteristics, depend on the type and conditions of the soil and are subject to spatial and temporal variations.Therefore, this research aimed to study the spatial variability and modeling of the spatial dependence of the coefficients of different infiltration equations in 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. The preliminary statistical checks involved determining the statistical summary, checking for normality and the presence or absence of trends in the penetration coefficients data, and were necessary, performing necessary transformations on the data. In order to check the spatial dependency of the data, the experimental semivariogram of the data was calculated and various theoretical models, including spherical, exponential and Gaussian models, were fitted to it and the best semivariogram model together with its characteristics were determined using statistical criteria. Coefficients in unmeasured points were also estimated using the normal kriging method and the inverse distance weighting (IDW) method with different weight strengths. 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 in the points without data and zoning was done using the appropriate estimation method. The statistical and geostatistical analyzes mentioned above were carried out with the software packages Excel and GS+.

Results and Discussion

The coefficient of variation (CV) of the examined infiltration equation coefficients varied between 12.5 and 478%, and the highest and lowest CV correspond to the coefficients “A” of the Kostiakov-Lewis (highest variability) and “b”' of the SCS equations (lowest variability). The model best fitted to the semivariogram of the coefficients of the Kostiakov equation (K and b), that of the Horton equation (c, m, and a), the “A” coefficients of the Philip equation and b' of the Kostiakov-Lewis equation was the isotropic spherical type; while the model best fitted to the coefficients of the SCS (a and b), the S coefficients of the Philip's equation and K and A of the Kostiakov-Lewis equation was of the isotropic exponential type. The changes range of the radius of influence of the coefficients of the infiltration equation was 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 nugget effect (C0) to threshold (C+C0) ratio, with a value of 0.648 was related to the coefficient “a” of the SCS equation, shows that 35.2% of the total variations have spatial structure; while 64.8% of the variations were random and without specific spatial structure. The lowest C0/(C+C0) ratio, with a value of 0.5 was related to the “b” coefficient of the SCS, the “C” and “a” coefficients of the Horton, “S” coefficient of the Philip, and the “b” coefficient of the Kostiakov equations, showing that 50% of their total variations are random (without spatial structure), and 50% are non-random and have spatial structure. The spatial correlation class of the infiltration equation coefficients was medium 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 accurate and the least accurate estimates were related to the “A” coefficient from Philip, “b” from Kostiakov, and “b'” of Kostiakov-Lewis equations, respectively.

Conclusion

In general, this study is suggested to use geostatistical methods and limited measurements to estimate the coefficients of the infiltration equations with reasonable accuracy and to save time and money when zoning of these coefficients or their values at many points is required. Of course, due to the weak and unsuitable spatial structure, the IDW was in some cases better suited than the kriging method in the studied area and its use can lead to more accurate estimates. Therefore, in cases where the spatial structure of the desired feature is weak and inappropriate, it is recommended that it is better not to use methods such as Kriging or other similar methods that rely on correlation and strong spatial structure, and in these cases, other alternative estimation methods, such as IDW which dose not depend on the presence of strong and appropriate spatial structure in the data should be used.