The relevance of Philip theory to Haverkamp quasi-exact implicit analytical formulation and its uses to predict soil hydraulic properties

Abstract

The quasi-exact implicit (QEI) analytical formulation of Haverkamp equation, which might be also known as Parlange model, and its one- and two-term approximate expansions are among the mostly used equations for in situ determination of soil sorptivity, S, and saturated hydraulic conductivity, Ks, from unsaturated one-dimensional (1D) cumulative infiltration into soils. However, from practical point of view, the approximate expansions are only valid from short to intermediate times and the QEI analytical formulation has a complex resolution, which makes its use complicated in inverting procedures. Therefore, alternative functions are needed to compute cumulative infiltration for longer times and improve inverting procedures for easier, more robust and accurate predictions of S and Ks. In this regard, current work presents and evaluates a new three-term approximation of the QEI analytical formulation. As a first step, we checked the accuracy of the proposed three-term approximate expansion with respect to the QEI formulation for three different soils (sand, loam and silt) in order to define its time domain validity. Next, the accuracy of the three-term approximate expansion to estimate S, Ks and the β parameter was compared to those obtained with one- and two-term approximate expansions. Lastly, a large dataset of field experimental data was inverted using the proposed three approximate expansions and the QEI analytical formulation, and goodness of fits predicted and measured cumulative infiltration curves and accuracy of the parameters (S, Ks and the β) estimates were compared. The results revealed that the three-term approximate has a larger validity time interval compared to one- and two-term approximate expansions, which allows its use for larger infiltration times durations resulting in more accurate estimates of Ks. Its capability of estimating S is also improved. The accurate prediction of β parameter is not still guaranteed for none of the approximate expansions. Compared to the one- and two-term approximate expansions, the experimental infiltration data usage revealed that the three-term approximate expansion resulted in higher performance and better prediction of hydraulic parameters.