Determining the soil hydraulic conductivity by means of a field scale internal drainage

Spatial variations of water content in large extents soils (vadose zone) are highly affected by the natural heterogeneity of the porous medium. This implies that the magnitude of the hydraulic properties, especially the conductivity, varies in an irregular manner with scale. Determining mean values of hydraulic properties will not suffice to accurately quantify water flow in the vadose zone. At field scale proper field measurements have to be carried out, similar to standard laboratory methods that also characterize the spatial variability of the hydraulic properties. Toward this aim an internal drainage test has been conducted at Ponticelli site near Naples (Italy) where water content and pressure head were monitored at 50 locations of a 2 x 50 m2 plot. The present paper illustrates a method to quantify the mean value and the spatial variability of the hydraulic parameters needed to calibrate the soil conductivity curve at field scale (hereafter defined as field scale hydraulic conductivity). A stochastic model that regards the hydraulic parameters as random space functions (RSFs) is derived by adopting the stream tube approach of Dagan and Bresler (1979). Owing to the randomness of the hydraulic parameters, even the water content theta will be a RSF whose mean value (hereafter termed field scale water content) is obtained as an ensemble average over all the realizations of a local analytical solution of Richards' equation. It is shown that the most frequent data collection should be carried out in the initial stage of the internal drainage experiment, when the most significant changes in water content occur. The model parameters are obtained by a standard least square optimization procedure using water content data at a certain depth (z = 30 cm) for several times (t = 5, 24, 48, 96, 144, 216, 312, 408, 576, 744, 912 h). The reliability of the proposed method is then evaluated by comparing the predicted water content with observations at different depths (z = 45, 60, 75, and 90 cm). The calibration procedure is further verified by comparing the cumulative distribution of measured water content at different times with corresponding distribution obtained from the calibrated model.