Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

Many different equations have been proposed to describe quantitatively one-dimensional soil water infiltration. The unknown coefficients of these characterize hydraulic properties and may be estimated from a n record, { t ∼ i , I } = 1 $\{ {\tilde t_i},{\tilde I_i}\} _{i 1}^n$ cumulative infiltration measurements using curve fitting techniques. two-term equation, ( ) S + c K s $I(t) S\sqrt c{K_{\rm{s}}}t$ Philip has widely used measured data. This function enjoys solid mathematical–physical underpinning admits closed-form solution for the sorptivity, [L T−1/2], multiple, [−], saturated conductivity, Ks T−1]. However, Philip's equation limited time validity, tvalid [T], thus data, $\tilde I(\tilde t)$ beyond valid $t {t_{{\rm{valid}}}}$ will corrupt estimates Ks. paper introduces novel method estimating S, c, Ks, equation. method, coined parasite inversion, use as vehicle Parlange's three-parameter As prerequisite our we present secondary contribution an exact, robust efficient numerical Bayesian parameter estimation with DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm yields byproduct marginal distribution β parameter. We evaluate 12 USDA types synthetic data simulated HYDRUS-1D. An excellent match is observed between inferred values their “true” known beforehand. Furthermore, correlate well texture, corroborate linearity $c({{\beta}})$ relationship 0 ≤ $0 \le fall within reported ranges. A vertical about 2.5 cm serve guideline time-validity