Analysis of 3D infiltration curves measured with disc infiltrometer in heterogeneous soil profiles: Sequential analysis of infiltration data and estimate of β

The 3-D Haverkamp et al. (1994) model for disc infiltrometer measures on homogeneous media involves the following parameters: the soil sorptivity, S, the saturated hydraulic conductivity, Ks, the β parameter and the A= (γ S²)/(r_d*Δθ) term, where r_d is the disc radius, Δθ is the soil water increase and γ is proportionality constant. Fixed β and A values are commonly used in most cases. S, and Ks can be estimated from the inverse analysis of a cumulative infiltration curve by fitting it the Haverkamp model. For practical reasons, Haverkamp implicit model is replaced by its 4-term (4T) approximate expansion for the transient state. The first part of this work analyzes the influence of layered soils on Ks and S estimates, and designs a new procedure, sequential Analysis of Infiltration curve (SAI), for treating infiltration curves impacted by soil layering. The SAI method analyzes a sequence of increasing dataset for a given infiltration curve and fits to the 4T expansions to estimate Ks, S. Then estimates and RMSE are reported as a function of the number of data points used for the fit. The method was applied on synthetic profiles with homogeneous loam soil, six layered profiles involving a 1, 2 and 3 cm thickness loam layer over silty or sandy loam soils, respectively. Erroneous estimates of Ks and S were obtained when the total infiltration curves were considered for the analysis, regardless of the presence of soil layering. In opposite, estimates were improved using the SAI method for the layered systems. The SAI method relies on the fact that the RMSE increases when the wetting front reaches the interface between the upper layer and the lower layer. Such increase allows (i) the detection of the soil heterogeneity, (ii) the determination of the optimum infiltration time, t_o, that corresponds to the minimum value of RMSE, and, (iii) accurate estimation the upper layer Ks and S.

Taking use of the SIA procedure, the second part of this communication studied the relationship between β and A, and proposed a new procedure to improve the estimate of Ks and S and approach β. The analysis was applied on synthetic infiltration curves simulated on homogneneous and layered columns. The results showed that different combinations of β and A resulted in similar Ks. Overall, optimization of Ks, S and A for different β values showed that β had an important effect on A and Ks, but not on S and RMSE.  We propose approaching the optimum β as the β for which is closer to zero, where A and A_exp are the optimized and measurable parameter, respectively. While the optimum β is calculated, Ks and S are computed by applying the optimum β to the respective quadratic β(Ks) and β(S) relationships. This methodology allowed improving the estimate of Ks giving good approaches of β (36% error) and omitting the erroneous praxis of using constant β and A values.

Haverkamp, R., et al. 1994. 3. Water Resources Research 30, 2931–2935.