Analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology

At the field scale, because of the relatively large number of observation points required to estimate the spatial distributions of hydraulic properties, application of inversion procedures must be based on a characteristic of the flow that for a given point in the field can be measured with relative ease, and can be used as input for the inversion procedure. Suggesting the use of infiltration data for this purpose, and recognizing the fact that a basic requirement for the design of a transient flow experiment is that the resulting inverse problem be sufficiently well posed to allow solution, this paper addresses the question under which circumstances the resulting inverse problem is well posed, utilizing the concepts of identifiability, uniqueness, and stability. For this purpose, three different models of the soil hydraulic properties were analyzed. The main conclusion of this study is that when infiltration data measured at the Darcy scale are used as input for the inversion procedure, the inclusion of prior information on a single measurable parameter, the saturated conductivity Ks, in the estimation criterion will enhance the likelihood of uniqueness and stability of the inverse solution provided that the structure of the hydraulic model is sufficiently simple. However, since for a particular situation, it is impossible to determine a priori whether the resultant inverse problem is well posed or not, this must be carried out only a posteriori by solving the problem several times with different initial parameter estimates, accompanied by an analysis of the associated estimation errors.

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