Approximate Solutions to Richards’ Equation for Soil Water Infiltration Using Scaling

Document Type : Research Article

Authors

• M. Sadeghi
• B. Ghahraman
• A.N. Ziaei
• K. Davary

10.22067/jsw.v0i0.26045

Abstract

After introducing similar media theory, many scaling methods were developed and have been widely used to cope with soil variability problem as well as to achieve invariant solutions of Richards’ equation. Recently, a method was developed for scaling Richards’ equation (RE) for dissimilar soils such that the scaled RE is independent of soil hydraulic properties for a wide range of soils. This method uses exponential – power hydraulic functions which are restricted to a limited range of soil-water content and matric potential. Hence, this method does not apply to the phenomena in which soil-water content and matric potential exceeds this range. Therefore, this research was performed to extend the method for a wider range of soil-water content and matric potential. This objective was achieved by modifying the exponential – power hydraulic functions and the scaling method was extended to the entire range of soil wetness (from saturated to dry). This study was followed to solve RE for soil-water infiltration using scaling. To do so, numerical solutions of the scaled RE was approximated by a scaled form of Philip three-term equation with soil-independent coefficients. The obtained approximate solution was tested using literature data of infiltration experiments on a sandy and two clayey soils. Results indicated that the solution can reasonably estimate (with the average relative error at most 9% for the cases studied here) measured infiltrated water. Also, it was shown that this solution can accurately approximate (with the average relative error at most 4% for the cases studied here) the numerical solutions of RE (for the same conditions and hydraulic functions). Hence, because of its simplicity, the solution is proposed as an alternative for numerical solutions of RE or other empirical equations for soil-water infiltration. Additionally, this solution can be easily applied to determine soil hydraulic functions by inverse solutions.

Keywords

• Variability
• Similar soils
• Dissimilar soils
• Exponential – power hydraulic functions

20.1001.1.20084757.1392.27.3.7.0

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