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Spatial Variability of Solute Leaching

Experimental Validation of a Quantitative Parameterization

^a Wageningen Univ., Dep. of Environmental Sci., Sub-dep. Water Resour., Nieuwe Kanaal 11, 6709 PA Wageningen, The Netherlands
^b Deakin Univ., School of Ecology and Environ., Center for Applied Dynamical Systems and Environmental Modelling, P.O. Box 423, Warrnambool Victoria, Australia 3280

View larger version (24K): [in a new window]   Fig. 1 The cumulative distribution function (cdf) given by the integral of the beta distribution function P defined in Eq. [1]. When the cdf is fitted to data of fractional solute leaching (sorted in descending order) with fractional sampling area, the slope P(z) at any point on the curve (represented by the straight line) equals the ratio of the infiltration area (Ai) over the outflow area (Ao). Hence, P(z) quantifies the severity of preferential flow for one stream tube. The coordinates define the fractions of the sampling plane (z) and the soil surface (cumulative probability density) occupied by streamtubes with stronger preferential flow than that corresponding to P(z)

View larger version (36K): [in a new window]   Fig. 2 Spatial distribution of chloride leaching from the lysimeter bottom. The center of the lysimeter is at . Each grid point represents a measurement location. The flat areas in the corners are outside the lysimeter cylinder. Average leaching (28.1 mmol Cl-) is indicated by the bold contour line. Cumulative leaching amounts in excess of the average have contour lines at multiples of 25 mmol Cl-

View larger version (55K): [in a new window]   Fig. 3 Observed and fitted fractions of leached chloride with either the fraction of the entire lysimeter bottom (a), or with the fraction of quadrants (b) and octants (c) of the bottom. The displayed quadrants and octants are those with the smallest and largest value of the HI (see Eq. [2])

View larger version (16K): [in a new window]   Fig. 4 The effect of the size of the individual sampling areas on the fitted values of and (Eq. [1]) and the HI (Eq. [2])

View larger version (21K): [in a new window]   Fig. 5 Observations and fitted curves for 2n sampling locations randomly selected from a total of 300. The curves for n 5 (including the observed and fitted curves for all 300 samples) are nearly identical

View larger version (16K): [in a new window]   Fig. 6 Fitted values of parameters and (Eq. [1]), as well as the HI (Eq. [2]) as a function of the number of sampling locations used in the fitting procedure

View larger version (50K): [in a new window]   Fig. 7 Fitted curves of the cumulative beta distribution function (a), and the beta distribution function P (see Eq. [1]) (b), for different sample sizes (cm2). The curves for flow in a uniform soil with 25% of the soil occupied by fingers and a uniform soil without fingering are included for comparison