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Soil Science Society of America Journal 66:384-395 (2002)
© 2002 Soil Science Society of America

DIVISION S-1—SOIL PHYSICS

Testing an Infiltration Method for Estimating Soil Hydraulic Properties in the Laboratory

L. Bruckler*,a, P. Bertuzzia, R. Angulo-Jaramillob and S. Ruya

a Institut National de la Recherche Agronomique, CSE Batiment Sols, Domaine Saint Paul, Site Agroparc, 84914 Montfavet Cedex 9, France
b Laboratoire d'Etude des Transferts en Hydrologie et Environnement, LTHE, UMR 5564 (CNRS, INPG, UJF), B.P.53, 38041 Grenoble Cédex 9, France

* Corresponding author (laurent.bruckler{at}avignon.inra.fr)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Solving soil unsaturated flow problems requires knowledge of the water retention, {theta}(h), and unsaturated hydraulic conductivity, K({theta}), relationships. The purpose of this study was to adapt to infiltration conditions the so-called Wind method previously described for evaporation conditions for determining {theta}(h) and K({theta}) and from laboratory cores. Infiltration in a vertical column of soil was first simulated using the numerical solution of Richards' equation for two soils. The simulated data were then used to evaluate the ability of the method to provide estimations of the hydraulic properties, whether measurement errors on tensiometric data were taken into account or not. In the laboratory, a sandy and a loamy soil sample were used in infiltration experiments. The experimental equipment consisted of (i) a metal cylinder containing the soil sample placed on an automatic balance, (ii) a set of tensiometers inserted in the soil sample, and (iii) a drip infiltrometer placed horizontally above the soil surface of the sample. Pressure head profiles and the weight of the sample was recorded at constant time steps. The infiltration method is able to provide estimates of the retention curve as was shown by numerical and laboratory experiments. Estimating the unsaturated hydraulic conductivity was possible by applying Wind's method to infiltration conditions, but as with the evaporation method, the variance of the hydraulic conductivity estimates was high.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
MODELING SOIL UNSATURATED FLOW and contaminant transport requires knowledge of soil hydraulic properties, namely water retention and unsaturated hydraulic conductivity. Steady state or instantaneous profile methods for measuring unsaturated hydraulic conductivity in a large water content domain (Vachaud et al., 1978) require local measurements of pressure head gradient and water contents in the soil. But accurately measuring local moisture content using specific techniques can be tedious or may disturb the soil sample. Therefore many researchers have focused on developing simple procedures such as inverse solution techniques or pedotransfer functions. Optimization techniques are now routinely used for estimating unsaturated soil hydraulic functions from laboratory outflow experiments, including more or less complicated situations like swelling soils or soils described with bimodal hydraulic functions (Zachmann et al., 1981; Dane and Hruska, 1983; Kool et al., 1985; Hudson et al., 1996; Garnier et al., 1997; Wildenschild et al., 1997; Zurmühl and Durner, 1998). Inverse procedures generally work correctly, although they strongly depend on the objective function, and the uniqueness of the solution may be in question. Recent application of neural network analysis to estimate soil hydraulic properties showed that artificial neural networks were generally efficient, especially when data were corrupted with small errors (Pachepsky et al., 1996; Tamari et al., 1996; Schaap et al., 1998).

Under evaporation conditions, Wind (1968) developed a simple method for determining the hydraulic properties of undisturbed soil samples in the laboratory. Tamari et al. (1993) found that the hydraulic properties determined with this method agreed well with those obtained with a reference method which required the pressure head and water content profiles at several time steps. Wendroth et al. (1993) evaluated the calculation procedure of the method for hydraulic properties with numerical simulations and confirmed the underlying theory and the limitations of the method at water contents near saturation. Moreover, it was found that the hydraulic parameters obtained with the Wind method corresponded closely to those estimated from the inverse technique within the range of [0 to -7 m] measured pressure heads (Simunek et al., 1998). Estimation of the water retention curves using the Wind algorithm was not very sensitive to experimental errors when tensiometric data were corrupted with small errors in their position or calibration, but small uncertainties in tensiometric data had a great influence on determining conductivity in wet conditions (Tamari et al., 1993; Mohrath et al., 1997).

Among the numerous methods that have been developed to estimate soil hydraulic properties (Stolte et al., 1994, Angulo-Jaramillo et al., 1996), the Wind method presents some advantages: (i) at any given time, only the mean water content of the soil sample is necessary instead of local measurements of water contents in the soil column, (ii) both the retention curve and the hydraulic conductivity–water content relationship may be simultaneously estimated, and (iii) because discrete values of unsaturated hydraulic conductivity and water content are calculated, no prescribed shape is necessary for the water content–hydraulic conductivity relationship. Nevertheless, the Wind method was previously only designed for evaporation experiments. The purpose of this study was to adapt the Wind procedure to infiltration and to describe the properties of the Wind method when applied to infiltration using both numerical simulations and experimental data. Indeed, although the Wind method is an old idea (Wind, 1968), its adaptation to infiltration conditions was never, after our knowledge, provided in the literature. However, evaluating the method in the infiltration case may be useful for several reasons:

  1. Because the soil hydrodynamic properties may be hysteretic, estimating both the water retention curve and the unsaturated hydraulic conductivity–water content relationship on the same disturbed or undisturbed soil sample, but under evaporation and infiltration conditions, makes it possible to describe the hysteresis of the soil hydrodynamic properties if the method performs well under evaporation as well as infiltration conditions.
  2. In the Wind method, the estimation of the unsaturated hydraulic conductivity–water content relationship and its accuracy depend on the shape of the water potential profile along the soil column, and consequently on the shape of the water content profile, which greatly differ between evaporation and infiltration conditions. Consequently, there is no evidence that the same method but applied to different surface water flux conditions (evaporation or infiltration) provides the same accuracy in the hydraulic conductivity–water content estimation.
  3. Water fluxes, and thus water content profiles, are more easily controlled under infiltration conditions with the drip infiltrometer than under free evaporation conditions.
  4. The duration of the experiment is significantly shorter under infiltration (few hours) than under evaporation (several days) conditions.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Estimating the Retention Curve
Wind (1968) proposed a simple experimental procedure where the mean water content of the whole column is required at several times instead of water content profiles. First, he used an assumed water retention curve to convert pressure head data at any one time into estimated water contents at the appropriate depths. Then, by making further assumptions on the shape of the water content profile in the soil sample, the mean water content of the soil sample was calculated and compared with the mean measured water content of the sample (Fig. 1) . If calculated and measured mean water content of the soil sample differed greatly, the water retention curve was optimized by an iterative procedure. After convergence of the algorithm, water contents at column depths corresponding to tensiometer locations were calculated from the measured pressure heads and the estimated water retention curve. In Wind's (1968) original algorithm, it is assumed that the sample can be divided into several layers with constant water content corresponding to the depths at which the pressure heads were measured. In a modified algorithm (Tamari et al., 1993), the water content profile at any one time is assumed to be given by a spline function describing the continuous water content profile from the top to the bottom of the soil sample. In this study however, we assume that an analytical model gives the shape of the water content profile for describing water content profiles during infiltration:

[1]
where {theta} (m3 m-3) is the volumetric water content and z (m) is the soil depth, and {theta}1 (m3 m-3), {theta}2 (m3 m-3), a1(m-1), and zm(m) are four parameters. To limit the number of parameters estimated at each time step, i.e., for each water content profile, an additional hypothesis was made:

[2]
where zn (m) is the depth of experimental water potential measurement with the last tensiometer (located above the bottom of the soil column), ti (s) is the time at which the water content profile is fitted, and {theta} (m3 m-3) is the volumetric water content coming from the combination of the water potential measurement at a given depth and of the retention curve estimated in the current iterative step. Parameters, {theta}1, a1, and zm of Eq. [1] were estimated by minimizing the sum of squared differences between modeled and estimated water content profiles. The Gauss–Marquardt algorithm was used to solve this least-squares optimization problem (Marquardt, 1963; Bard, 1974). Iterations were stopped when either the relative difference of the sums of squares or the relative variation of estimated parameter values was <10-4 between two successive iterations (both criteria were examined simultaneously).



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  		Fig. 1. Schematic representation of Wind's procedure for estimating the retention curve and the hydraulic conductivity–water content relationship under infiltration conditions (we and wm are gravimetric or volumetric water contents).

 
The water retention curve of the soil is assumed to be an S-shaped function as proposed by van Genuchten (1980):

[3]
with m = 1 - and where h (m) is the pore-water pressure head and {theta} is the volumetric water content (m3 m-3). This expression uses four parameters: {theta}s, saturated water content (m3 m-3), {theta}r, residual water content (m3 m-3), {alpha} (m-1), and n. Parameters of Eq. [3] were estimated with the Gauss-Marquardt algorithm (Marquardt, 1963; Bard, 1974) by minimizing the sum of squared differences between modeled and estimated mean water contents of the whole soil sample over a range of water contents, i.e., at different times.

Estimating the Unsaturated Hydraulic Conductivity
After estimating the retention curve, unsaturated hydraulic conductivity was determined from measurements of pressure heads and water content estimates in the sample at several depths and times, using the instantaneous profile method (Tamari et al., 1993; Mohrath et al., 1997).

According to the Darcy law,

[4]
where qz (m s-1) is the water flux density, K({theta}) (m s-1) is the unsaturated hydraulic conductivity relationship, and {partial}h/{partial}z the pressure head gradient at depth z (m), the unsaturated hydraulic conductivity was estimated by:

[5]

The water flux through depth z is calculated from:

[6]
where qz and qz+1 (m s-1) are the water fluxes at two consecutive depths z and z + 1 (z0 and zz max correspond to the top and the bottom of the soil column, respectively), {Delta}S (m3) is the change in water storage in a finite elementary soil layer having a surface Scol between times t and t + {Delta}t, and is calculated from the soil moisture profiles as calculated before. The pressure head gradient {Delta}h/{Delta}z is estimated from a three-point approximation as follows: First, the mean pressure heads (z - 1)t,t+{Delta}t, (z)t,t+{Delta}t, (z + 1)t,t+{Delta}t between two consecutive times are calculated at three consecutive depths, z - 1, z, z + 1. The mean water potentials between, z - 1, z, z + 1, are then calculated as an arithmetic mean,

[7]

The pressure head gradient {Delta}h/{Delta}z at depth z is finally estimated by:

[8]
where {Delta}z is the distance between the center of the (z - 1, z) and (z, z + 1) soil layers. The proposed procedure for calculating hydraulic conductivity provides pairs of (Ki,j,{theta}i,j) estimates, where the subscripts i,j refer to depth and time, respectively. In Wind's approach, the estimates (Ki,j,{theta}i,j) can be fitted to any analytical model after calculation, but basically, this additional fitting procedure is not useful for calculations.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Numerical Experiments and Error Analysis
Infiltration in a vertical column of soil (150 mm in diam., 72 mm in height) was first simulated for a homogeneous soil column. Equation [3] was used for the retention curve, whereas a Mualem–van Genuchten model (van Genuchten, 1980) was used as input for the hydraulic conductivity vs. water content relationship. Two soil types with different hydrodynamic properties were studied (Tables 1 and 2), a sand and a loam with a continuous soil structure. For both soils, the parameter l in the Mualem–van Genuchten equation (tortuosity parameter) was set to the value 0.5. The water transport equation was solved using the pressure head as a dependent variable, by a Galerkin finite element method with linear elements, which varied from 0.5 mm at the soil surface to 1 mm at the bottom of the profile. A fully implicit scheme was used to advance the solution in time with automatically varying time steps (between 0.1 and 10 s). The maximum relative convergence criterion for pressure head calculations was 1 x 10-3. Instantaneous relative errors in the mass balance were <1 x 10-4, whereas cumulative relative errors in the mass balance at the end of calculations were <0.5% for the two soils. The bulk density of the soil column equaled 1430 and 1550 kg m-3 for the sand and the loamy soil, respectively. The initial condition for the simulations was hydraulic equilibrium at a hydraulic head of -1.5 and -10 m for the sandy soil and the loam, respectively, and a zero-flux condition was imposed at the bottom of the sample. Infiltration rate was constant and equaled 3 and 1.5 mm h-1 for the sand and the loamy soil, respectively. These infiltration rates were chosen to simulate a relatively low infiltration experiment and to obtain sufficient data to apply the Wind method. The range of simulated water contents was [0.093–0.392 m3 m-3] and [0.200–0.394 m3 m-3], which corresponded to the [-1.5, -0.30 m] and [-10, -2.3 m] pressure head ranges for the sand and loam, respectively. Numerical simulations provided pressure head values at various selected times and depths (19, 26, 37, 52, and 67 mm), and mean volumetric water content of the whole soil column at the same times. The simulated pressure head gradient differed greatly between the two soils because of their contrasted hydraulic properties. After 1-h infiltration, the mean water potential gradient in the first centimeter of the soil column was 2.3 and 92.9 m m-1 for sand and loam, respectively. The simulated data were then used to evaluate the suitability of the method for providing estimations of the retention curve and of unsaturated conductivity.


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  		Table 1. Estimated parameters of the retention curve for the sandy and loamy soils used in the simulations (according to the functions of Van Genuchten (1980)). The saturated water content, {theta}s, is not estimated and set at its true value. The change in pressure head, {Delta}h, is the maximum measurement error on tensiometric data.

 

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  		Table 2. Estimated parameters of the hydraulic conductivity–water content relationship for the sandy and loamy soils used in the simulations (according to the functions of Van Genuchten (1980)). The saturated water content, {theta}s, is not estimated and set at its true value, the parameter l in the Mualem–van Genuchten equation (tortuosity parameter) is set at its value (0.5) and not estimated. The change in pressure head, {Delta}h, is the maximum measurement error on tensiometric data.

 
Because pressure head gradients are small near saturation, and, thus, very sensitive to uncertainties in tensiometric data, error propagation on hydraulic properties also has to be estimated. To simulate tensiometric measurement errors, calculated pressure heads were randomly corrupted with noise by adding a term distributed in the [-{Delta}h, +{Delta}h] interval with a {Delta}h value of 2 x10-3 or 5 x 10-3 m. Absolute errors in tensiometric measurements corresponded to relative errors of 0.2 to 0.02% and of 0.5 to 0.05% for pressure heads varying from -1 to -10 m, and for {Delta}h = 2 x 10-3 or {Delta}h = 5 x 10-3 m, respectively. The corrupted data sets were then used to evaluate the suitability of the method for estimating the retention curve and unsaturated conductivity under infiltration conditions and when experimental measurement errors on pressure heads were taken into account.

Experimental Design
The experimental equipment consisted of (i) a metal cylinder (150-mm i.d., 72-mm height) containing the soil sample and placed on an automatic weighing device connected to a microcomputer, (ii) a set of tensiometers inserted in the soil sample, connected to pressure transducers (model 32-015-D, GS Sensors, Les Clayes sous Bois, France) and recorded on a data logger (Campbell CR 10X, Campbell Scientific, Leicestershire, UK), and (iii) a drip infiltrometer placed horizontally above the soil surface of the sample (Fig. 2) . The metal cylinder had small holes (2 mm in diam.) located at six depths (5, 10, 15, 30, 50, and 65 mm) in which the porous ceramic cups (20 mm long and 2 mm in diam.) of the tensiometers (SDEC, Reignac, France) were horizontally inserted. Calibration curves of the pressure transducers were made in the laboratory and were linear between 0 and -8 m. They were performed at three temperatures (15, 25, and 35°C), and temperature effects were directly incorporated in the linear coefficients of the regression lines which were then temperature dependent. The stability of the transducers was ±2 mm (95% confidence interval) over several days. Before starting the infiltration experiment, porous ceramic cups and capillary tubes were filled with previously boiled water, thus having a low dissolved gas concentration. Pressure head profiles were recorded at constant time steps and data measured at the end of the experiment were transmitted to the microcomputer for recording and displaying. At the same time as the tensiometric data were recorded, the sample was weighed on the automatic scales. Mean water contents of the whole soil column were computed from measurements taken when the samples were weighed and from dry mass determination of the soil measured at the end of the experiment. The drip infiltrometer was made of small needles (0.24-mm i.d.) regularly located on a squared grid (2.5-cm spacing between needles). The needles were connected to a pump, which could provide water fluxes at the soil surface varying from 0.7 to 504 mm h-1 (between 1 and 120 pulses per min) with demineralized water. Preliminary analysis of the technical performances of the drip infiltrometer showed that for infiltration fluxes >0.7 mm h-1, the water flux was constant over time and that the homogeneity of spatial water distribution at the soil surface was satisfactory. Indeed, dividing the soil surface into four equal zones and assuming that the greatest water flux observed was set at one, measurements indicated that the water fluxes equaled 0.94, 0.94, 0.96, and 1.00 among the four zones, respectively. To select an order of magnitude of the infiltration rate, consider a soil sample having a water content at saturation of ~0.45 m3 m-3, and an initial water content between 0.20 and 0.30 m3 m-3. Starting the experiment with an infiltration rate of 3 mm h-1 will lead to the saturation of the soil sample after 6.0 and 3.6 h, respectively. This duration is sufficient to record numerous experimental data (recording time step of 20 s) to apply the Wind method. Consequently, according to a practical point of view, infiltration rates of ~3 mm h-1 are recommended, leading to regular and homogeneous water fluxes in time and space, and providing numerous experimental records for applying the Wind method.



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  		Fig. 2. Schematic representation of the experimental design: (1) pulsing pump, (2) drip infiltrometer, (3) soil cylinder, (4) microtensiometers, (5) electronic unit, (6) weighing device, (7) multiplexer, (8) datalogger, and (9) microcomputer.

 
Soil Samples and Measurements
Two soil samples were used; first, a sandy soil (98.5% SiO2, 100% of mineral particles between 0.050 and 0.200 mm) was used. After screening the mineral particles (<0.1 mm), the soil was prepared in the metal cylinder. Successive soil layers (500 g per soil layer) were compacted at a volumetric water content of 0.16 m3 m-3 to obtain an optimum homogeneity of the soil column and to a mean bulk density of 1.429 g cm-3. Second, a loamy soil (16.0% clay, 46.6% silt, 37.4% sand) having a mean bulk density of 1.632 g cm-3 was used. The soil sample was taken directly from the field and undisturbed. Before the infiltration experiments, the soil samples were covered with a plastic sheet and left for several days in the laboratory to reach a water potential equilibrium in the soil column. Thus, before starting the infiltration, the soil water potentials from the top to the bottom of the columns were in the range [-1.6, -1.4 m] and [-6.8, -7.6 m] for the sandy and loamy soils, respectively. For the sandy soil, the infiltration experiment lasted 6 h with an infiltration rate of 3 mm h-1 and the time step for recording the mass of the soil column and tensiometric data of 30 s. For the loamy soil, the infiltration experiment lasted 2 h with an infiltration rate of 4 mm h-1 and the time step for recording the mass of the soil column and tensiometric data of 20 s. Absolute errors associated with pressure heads given by the tensiometric measurements were <5 mm. For each soil sample, the saturated hydraulic conductivity was measured with a constant pressure head permeameter using demineralized water after a 3-d saturation of the soil samples. A linear relationship was found between the pressure head and the water flux, and the measured saturated hydraulic conductivity was 4.62 x 10-5 and 4.97 x 10-5 m s-1 for the sandy and loamy soil, respectively.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
Estimating the Hydraulic Properties from Numerical Experiments
For the sand, the infiltration front is visible during the first 2 h (Fig. 3a) , whereas the influence of gravitational water potential increases with time, thus leading to greater soil matric potential at the bottom of the column than at the top, and to the accumulation of water at the bottom of the soil column after 2 h. For the loam, the infiltration front is visible throughout the overall duration of the simulation (Fig. 3b), and the influence of gravitational water potential remains negligible until the end of the infiltration period.



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  		Fig. 3. Simulated water potential versus time at several depths in a soil column under infiltration conditions (a) sandy soil (b) loamy soil.

 
For both soils, the saturated water content ({theta}s) was set at its actual value and not estimated, because it is generally known from basic physical characteristics of the soil cores. Also, to limit the number of parameters to be estimated for the unsaturated hydraulic conductivity, the parameter l in the Mualem–van Genuchten equation (tortuosity parameter) was set at its value 0.5 and not estimated. When no measurement errors on tensiometric data were taken into account, all three parameters of the water retention curve ({theta}r, {alpha}, and n) were estimated accurately (Table 1). For both soils, results were regarded as satisfactory, especially in the wet zone for which the water content–water potential relationship was correctly described as shown in Fig. 4a and b . For drier conditions, small discrepancies between the true and the fitted retention curves appeared, and this was because of the fact that under infiltration conditions more data are available in wet conditions or near the saturation of the soil sample than in dry conditions. With computed pressure heads corrupted by adding a distributed noise in the [-{Delta}h, +{Delta}h] interval, estimation of the water retention curves was still good (Table 1), and thus, estimation of the retention curve using the Wind method was not very sensitive to experimental errors. For the loamy soil, the consequences of measurement errors were negligible on the estimated parameters of the retention curve (Table 1). For the sandy soil, parameter change was more significant (Table 1). These results are in agreement with results of Tamari et al. (1993) and Mohrath et al. (1997) who showed that the estimation of the water retention curves was slightly sensitive to errors because of the method itself or to tensiometric measurements.



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  		Fig. 4. Comparison between the theoretical (dotted line) and estimated (continuous line) retention curves in numerical experiments with the infiltration method without measurement errors on tensiometric data (a) sandy soil (b) loamy soil.

 
Figure 5a and b compare the simulated water content profiles from the finite-element solution of Richard's equation with the fitted water content profiles according to Eq. [1]. Results show that the shape of the profiles is generally correctly fitted. When measurement errors on tensiometric data are taken into account , differences between simulated and fitted water content are <0.002 and 0.004 m3 m-3 for the sand and the loam, respectively (Fig. 6a and b) . However, small differences between the fitted and simulated water contents may be sufficient to incorrectly estimate both the changes in water content between two times, and consequently the water flux at a given depth (Eq. [6]), and the water potential gradients in the column (Eq. [8]), thus leading to meaningless estimates of hydraulic conductivity (Tamari et al., 1993).



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  		Fig. 5. Simulated (symbols) and fitted (continuous line) water content profiles at several times in a soil column under infiltration conditions (a) sandy soil (b) loamy soil.

 


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  		Fig. 6. Residuals (m3 m-3) of the water content profile fitting according to Eq. [1] during the simulated infiltration (a) sandy soil (b) loamy soil.

 
Without measurement errors on tensiometric data, the general shape of the water content–hydraulic conductivity relationship was correctly described for the sand (Fig. 7a) and the loam (Fig. 8a) , although some discrepancies existed between the true and estimated data. This indicated that without errors, the estimation procedure provided some bias in estimating the hydraulic conductivity (Table 2). This appears to be an effect of the fitting procedure of the water content profiles, which could cause inaccuracies in estimating the actual water flux at a given depth and the actual water potential gradient. The differences between the estimated hydraulic conductivity and the true values depended on the depth where calculations were made. This was because of the fact that the fitness of the water content profiles versus time depended on the depth in the soil profile (Fig. 6a and b), thus leading to hydraulic conductivity estimates of varying quality. Indeed, the shape of the water content profiles changes in time and the quality of the fitting curve for the water content profiles (Eq. [1]) may depend on this shape.



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  		Fig. 7. Comparison between the theoretical (continuous line) and estimated (symbols) hydraulic conductivity–water content relationship in numerical experiments with the infiltration method for the sandy soil (a) no error on tensiometric measurements (b) ± 2 x 10-3 m on tensiometric measurements (c) ± 5 x 10-3 m on tensiometric measurements.

 


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  		Fig. 8. Comparison between the theoretical (continuous line) and estimated (symbols) hydraulic conductivity–water content relationship in numerical experiments with the infiltration method for the loamy soil (a) no error on tensiometric measurements (b) ± 2 x 10-3 m on tensiometric measurements (c) ± 5 x10-3 m on tensiometric measurements conditions.

 
The infiltration version is here restricted to the situation that the bottom compartment is not saturated, this results in the case of the sandy soil in determination of the hydraulic properties over a limited range in pressure heads or water content (~0.05 m3 m-3). Indeed, a similar situation was found under evaporation conditions (Tamari et al., 1993); in the case where hydraulic conductivities were estimated taking into account uncertainties in the tensiometric and weight data, and with hydraulic head gradients different from zero at the 0.01 probability level, the water content range for estimating the hydraulic conductivity was 0.05 m3 m-3. Thus, for both evaporation and infiltration conditions, but for different reasons (water accumulation in the infiltration case, water potential gradients near zero in the column in the evaporation case), the estimation of the hydraulic conductivity–water content relationship is only possible over a limited range in pressure heads or water content for soils having a high hydraulic conductivity like sandy soils.

Comparing conductivity data determined with or without error measurements (Fig. 7a, b, c, and 8a, b, and c) shows how uncertainties in tensiometric data have an influence on the conductivity determination. Errors in hydraulic conductivity could be of one order of magnitude or less, and estimated parameters of the water content–hydraulic conductivity relationship varied progressively when {Delta}h increased (Table 2). Changes in the estimated parameters were greater for the sand for which a small water content domain was available (0.05 m3 m-3). These results are in agreement with previous results which showed that small uncertainties in tensiometric data had a great influence on determining conductivity under evaporation conditions (Tamari et al., 1993; Mohrath et al., 1997).

Estimating the Hydraulic Properties from Experiments
The infiltration front was visible during the first 2 h of the experiments for the sandy soil, whereas small water potential gradients existed afterwards, because of gravitational water potential that led to water accumulation in the bottom of the soil column. A rapid increase of the water potential at the end of the experiment corresponded to the near-saturation zone of the retention curve with very small capillary capacity. Because the numerical experiments showed that the estimation of the water retention curves was slightly sensitive to errors because of the method itself or to tensiometric measurements, only the hydraulic conductivity estimates are discussed. For the sandy soil (Fig. 9) , the estimated hydraulic conductivity data are approximately in the [1 x 10-5, 1 x 10-8 m s-1] range. The general shape of the hydraulic conductivity–water content relationship was fitted according to the model of van Genuchten (1980), although a great variability in the estimated hydraulic conductivities was found. In agreement with results presented above, this was mainly because of propagation errors from tensiometric measurements and from the water content profile fitting procedure. For the loamy soil, the estimated hydraulic conductivity data are approximately in the [1 x 10-5, 1 x 10-9 m s-1] range. The general shape of the hydraulic conductivity–water content (Fig. 10a) and hydraulic conductivity–water potential (Fig. 10b) relationships were correctly fitted according to the model of van Genuchten (1980), and showed a rapid decrease of the hydraulic conductivity near saturation. In agreement with results presented above, a significant variability in the estimated hydraulic conductivities was found. For both soils, the mean fitting of the hydraulic conductivity curves with water content or water potential agrees well with the independent measurement of saturated hydraulic conductivity. Indeed, the estimated saturated conductivities from the curve fitting are 11.4 x 10-5 and 7.8 x 10-5 m s-1, whereas the measured values are 4.6 x 10-5 and 5.0 x 10-5 m s-1, for the sandy and loamy soil, respectively. Results indicate a high variance of the hydraulic conductivity estimates, especially under wet conditions for the sand. This is partly because of relative errors in water potential gradients, which become greater as the water content increases during infiltration. Assuming that the random variable ({partial}{phi}/{partial}z)|z is normal, Kz is then described by the 1/N (µ, {sigma}) distribution function (Eq. [5]), it was shown that when the ratio ({sigma}/µ) for the pressure head gradient ({partial}{phi}/{partial}z)|z is great (wet soils), the change in sign of the gradients could create physically meaningless Kz values, and errors in the gradient term cause a strongly asymmetrical and discontinuous Kz distribution (Flühler et al., 1976; Tamari et al., 1993). In such a case, the underlying assumption of normal distribution of Kz for error analysis is wrong in principle. Differences in the hydraulic conductivity estimates depending on the depth in the soil column where the estimation was made also exist, and this may be because of small errors in measuring the accurate depth of the tensiometers in the soil as Mohrath et al. (1997) demonstrated with Wind's method.



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  		Fig. 9. Estimated hydraulic conductivity–water content relationship with Wind's method under infiltration conditions for the sandy soil. The parameter {theta}s is not estimated and set to its true value and the Ksat point is an independent measurement.

 


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  		Fig. 10. Estimated hydraulic conductivity–water content (a) and hydraulic conductivity–water potential (b) relationships with Wind's method under infiltration conditions for the loamy soil. The parameter {theta}s is not estimated and set to its true value and the Ksat point is an independent measurement.

 

   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
This study analyzed an adaptation of a simple evaporation method to infiltration conditions for estimating hydraulic properties in the laboratory. Basically, Wind's method uses pressure heads and the mean water contents of the whole column at several times. Using numerical and laboratory experiments, several conclusions can be drawn. The infiltration method is able to provide satisfactory estimates of the retention curve as was shown by both numerical experiments. Estimating the hydraulic conductivity was possible in principle and roughly satisfactory, but the method showed some limitations. Theoretical results indicated that meaningless values of hydraulic conductivities could be found when water content profiles were not fitted with great accuracy and small water potential gradients existed. Experimental results were encouraging but indicated that, as with the evaporation method, variance of the estimated hydraulic conductivity increased with water content, when water potential gradients decreased. Nevertheless, the method can be used for disturbed and undisturbed soil samples, and evaporation or infiltration boundary conditions may theoretically be applied to the same soil column, thus providing data on hysteresis of soil properties. Adding a model for hysteresis in the estimation procedure of the retention curve could improve the method. Moreover, this method may complete other methods such as optimization procedures when the selected shape of the hydraulic conductivity–water content is not valid, or tension disk infiltrometers when soil tension is lower than -0.15 m.


   ACKNOWLEDGMENTS
 
We are grateful to C. Young from the INRA Translation and Terminology Department for help with the manuscript, and to D. Mohrath, O. Martin, and A. Kaprelian for their technical assistance.

Received for publication March 22, 2001.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 




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