Geostatistics were used to describe the spatial variability of hydraulic ... was carded out using Geostatistics (Journel and Huijbregts, 1978; ASCE Task.
Geoderma, 60 (1993) 169-186 Elsevier Science Publishers B.V., Amsterdam
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Use of an inverse method and geostatistics to estimate soil hydraulic conductivity for spatial variability analysis Nunzio Romano Institute of Agricultural Hydraulics, University of Naples "FedericoII", Via Universitl~ 100, 80055 Portici, Naples, Italy (Received September 9, 1992; accepted after revision October 23, 1992)
ABSTRACT A field method for determining the soil hydraulic properties using a parameter estimation technique is presented. Input data for the inverse problem are soil-water potentials and soil-water contents measured at different soil depths and different times during a field transient drainage experiment. For the water retention function the parametric relation suggested by Van Genuchten was adopted. For the hydraulic conductivity function the relation proposed by Van Genuchten and the exponential relation were adopted. With the proposed method soil hydraulic properties along a transect of a volcanic Vesuvian soil were determined using as boundary condition the unit gradient of total potential at the bottom of the soil profile. Geostatistics were used to describe the spatial variability of hydraulic conductivity characteristics of the soil here considered. Finally, results obtained using this method were compared with those of the simplified method suggested by Sisson and Van Genuchten based on a unit gradient water flow model.
INTRODUCTION
The reliability of the results with numerical models developed for simulating unsaturated flow and transport processes is chiefly linked to the accuracy with which soil hydraulic properties are determined. A proper use of models on a large scale also requires knowledge of spatial and temporal variability of these properties (Warrick and Nielsen, 1980). In particular, in order that models may provide accurate responses which can be put into practice, it is necessary to set up methods enabling an appropriate and complete description of soil hydraulic conductivity behaviour. In the last few years, researchers have shown that the water retention and hydraulic conductivity functions may be determined simultaneously by means of more straightforward transient tests. Inversion of the governing equation is performed through numerical techniques and optimization algorithms. Even though it requires a large number of calculations, this approach allows greater 0016-7061/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
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flexibility in the choice of experimental tests to be performed in the field and enables the confidence intervals for the estimated parameter values to be defined (Kool et al., 1987). Santini and Romano ( 1992 ) set up a method to solve the inverse problem of determining in-situ soil hydraulic properties from a transient drainage experiment by a parameter estimation technique. In the present study, this method was used to determine the hydraulic properties along a transect of a typical volcanic soil of the Campania Plain and spatial variability analysis was carded out using Geostatistics (Journel and Huijbregts, 1978; ASCE Task Committee, 1990). Since reliable soil hydraulic conductivity measurements are difficult to obtain and show great spatial variability, several researchers have proposed simplified methods to estimate hydraulic conductivity functions (Davidson et al., 1969; Jones and Wagenet, 1984; Green et al., 1986; Vauclin and Vachaud, 1987 ). However, these methods can provide only rough estimates of average values of soil hydraulic conductivity over large areas and could lead to some prediction errors using numerical models which allow a more detailed description of water and chemical transport in soil (Wagenet and Addiscott, 1987 ). Moreover, these errors could have considerable weight in studying the structure of spatial variation of hydraulic conductivity using statistical or geostatistical techniques, because they could mask statistically significant relations between hydraulic conductivity and position of sampling points. Therefore, the purpose of this study was also to compare estimates of unsaturated hydraulic conductivity values and their spatial variability along the transect obtained using the proposed method with those of the simplified method suggested by Sisson and Van Genuchten (1991 ) based on the assumption of unit gradient of the total soil-water potential. METHODOLOGY
Hydraulic properties of the soil in question were determined by the simplified field method of Sisson and Van Genuchten ( 1991 ). These authors developed a nonlinear least-squares parameter optimization program Ungra to estimate the unknown parameters in the well-known hydraulic model suggested by Van Genuchten (1980) (referred to hereafter as the UVG model). In addition, soil hydraulic properties were also determined by using a more rigorous field method set up by Santini and Romano (1992). The proposed method for determining simultaneously soil hydraulic properties by a parameter estimation approach involves in-situ measurements of soil-water potentials h and volumetric soil-water contents 0 during a transient drainage experiment. The partial differential equation governing transient one-dimensional unsaturated flow in a porous medium is:
FIELD METHOD FOR DETERMINING SOIL HYDRAULIC PROPERTIES
Oh
0
171
Oh
where C(h) is the soil-water capacity, t is the time and z is the vertical distance from the soil surface, positive downward (Hillel, 1980; Jury et al., 1991 ). The C(h) and k(h) functions were described by means of analytical relations for the water retention 0 (h) and hydraulic conductivity k (0) functions. The soil-water retention function used in this study is given by (Van Genuchten, 1980): O(h) =Or+ ( 0 s - 0 r ) [ 1 + I a h l " ] _m
(2)
where 0s and Orare the saturated and residual water contents, respectivily, and a, n and m are empirical parameters. Introducing eq. (2) in Mualem's model (1976) with the condition m = 1 - 1/n, Van Genuchten (1980) derived the dosed-form relation for the hydraulic conductivity function:
k(0) = k ~ S ° ' [ 1 - (1 -S'£m)m] 2
(3)
where Se = ( 0 - Or) / ( 0s- Or) is the effective saturation and ks is the hydraulic conductivity when 0= 0~. Together with eq. (3), in this study the hydraulic conductivity function is also assumed to be described by the exponential relation (Davidson et al., 1969): k( O) --l~ exp[fl( O-O~) ]
(4)
where fl is an empirical parameter related to the particle size distribution. Relation (4) was widely used for estimating soil hydraulic conductivity by means of simplified methods (Sisson et al., 1980; Jones and Wagenet, 1984; Wagenet and Addiscott, 1987) and provided good results for many soils tested at our Institute (Santini and Ciollaro, 1988; Romano, 1990). Inversion of eq. (1) requires specification of the initial condition and boundary conditions both at the soil surface (z=0) and the bottom of the soil profile (z=L). At the beginning of drainage and at the upper boundary of the flow domain, the following conditions express in analytical terms experimental situations: h(z) =0 Oh/Oz=l
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DISTANCE ALONG THE TRANSECT (m) Fig. 3. Values of soil hydraulic conductivity k at 1 m intervals along the 50 m transect at water content 0=0.35 (a), 0=0.30 (b), and 0=0.20 (c). Dashed lines with open squares and solid lines with open circles indicate k(O) values estimated by the proposed method using the VG and EXP models, respectively. Dashed-dotted lines with solid triangles indicate k(0) values estimated using the UVG model with the computer code Ungra written by Sisson and Van Genuchten.
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Fig. 4. Experimental semivariogram for soil hydraulic conductivity values k at 0=0.35 (a), 0= 0.30 (b), and 0 = 0.20 (c) estimated by the proposed method using the VG model and transformed into logarithms.
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