Explicit formulae for soil water diffusivity using the one-step outflow technique

One of the most widely used methods in determining soil water diffusivity, D, as a function of the volumetric water content, theta, is the one-step outflow method. Unfortunately, the calculation of D(theta) according to direct methods usually requires the estimation of the first and second derivative of the outflow volume, V, dV/dt and d(2)V/dt(2) of the original measured cumulative outflow data V(t). These derivatives are usually approximated by applying a finite difference technique to two or three consecutive outflow measurements. Therefore, the accuracy of the results depends essentially on the accuracy of local outflow measurements. Inaccuracies are more intensive in the last portion of the outflow curve, where small errors of measurement may yield large inaccuracies in the first and second derivatives of the outflow curve. Furthermore, the entire calculation procedure for estimating dV/dt and d(2)V/dt(2) is rather laborious and complicated. We developed a direct method based on a simple curve-fitting procedure applied to the experimental outflow data for a simple power and an extended power form function, which leads to direct calculation of the soil water diffusivity function from explicit formulae. The only parameters involved in these formulae are the empirical parameters obtained by the curve-fitting procedure. The proposed method was verified from one-step outflow experiments performed in nine porous materials (one sand, two soils, and six substrate mixtures). Comparison with previous methods indicated a good performance of the proposed explicit algebraic formulae.