Inverse Estimations of Soil Hydraulic Properties with Scaling: One‐Dimensional Infiltration

Inverse estimations of hydraulic properties are of immense importance to effectively provide input for water flow modeling and descriptions of soil systems. Here inverse estimations were made using scaled forms of Richards' equation and infiltration measurements in two steps. In Step 1, transient experimental data of cumulative infiltration rate, or wetting front position were “best‐fit” using Philip's quasi‐analytical, algebraic forms. This was demonstrated with linear regression although a maximum likelibood method could have been used. The first step does not depend on the form of the hydraulic functions and is valid for all uniform soils with constant initial and boundary conditions. Step 2 related the algebraic coefficients to the soil properties and was dependent on the model assumed for the hydraulic functions. Computations were generally algebraic and extremely easy relative to alternative methods that require a numerical simulation for each combination of properties considered. Clearly, the number of estimated parameters cannot exceed the significant number of terms fit to the algebraic forms. For small times or “noisy” data, perhaps only one parameter can be estimated that, for the examples presented, leads to an estimate of the ratio of saturated conductivity to an inverse characteristic length. For this situation, further measurements are needed to provide additional information if more parameters are to be found. Three commonly used forms of hydraulic functions were used, but the methodology is not limited to these specific forms. Scaling could also be used for more complex geometrics and moisture regimes; however, the convenience of the algebraic forms will not generally be available in those cases.