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Published in Vadose Zone Journal 2:358-367 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH PAPER

Field Testing Parameter Sensitivity of the Two-Term Infiltration Equation Using Differentiated Linearization

Vincenzo Bagarello and Massimo Iovino*

Dipartimento di Ingegneria e Tecnologie Agro-Forestali, Università degli Studi di Palermo, Facoltà di Agraria, Viale delle Scienze, 90128, Palermo, Italy
* Corresponding author (iovinom{at}unipa.it).

1 Mention of a product does not constitute endorsement by the University of Palermo or by the authors. Back


Received 18 October 2002.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Knowledge of the hydraulic conductivity of the vadose zone is important in many agronomic, engineering, and environmental areas. Transient tension infiltrometer experiments can be used to estimate the hydraulic conductivity, K0, corresponding to a given pressure head by a transient single-test (TST) method that uses the coefficients C1 and C2 of the two-term infiltration equation. A differentiated linearization (DL) method was previously proposed to estimate these coefficients when a layer of contact material is used for the experiment. A field test of the DL and TST methods was conducted on a sandy loam and a clay soil. Eliminating the early-time influence of the contact layer was easy when the sorptivity of the contact material was 10 to 12 times higher than the soil sorptivity. In other cases a transition zone, which complicated application of the DL method, appeared between the decreasing and increasing portions of the data set. Therefore, applicability of the DL method required large differences in capillary forces between the contact material and the soil. Estimates of K0 varied by up to 650% with the duration of the experiment and <50% with the time interval between readings at the water reservoir. Sensitivity of K0 to the experiment duration was particularly remarkable for the sandy loam soil for short durations. Considering a minimum duration of the experiment of approximately 1 h caused estimates of K0 to vary by a maximum of 40% with the duration of the experiment.

Abbreviations: CI, cumulative infiltration [method] • DL, differentiated linearization [method] • SST, steady-state single test [method] • TST, transient single-test [method]


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
KNOWLEDGE OF SOIL hydraulic conductivity, K, of the vadose zone is critically important in many agronomic, engineering, and environmental areas. For example, it is essential to predict water infiltration into soil, to model water and solute transport processes, including migration of pollutants from contaminated sites to groundwater, and to evaluate soil physical quality. The hydraulic conductivity of saturated or near-saturated soil can be estimated using different methods. Choosing the proper measurement method and the proper application procedure for the selected method is essential to obtain accurate estimates of K (Reynolds et al., 2000; Vandervaere et al., 2000b). The Guelph permeameter (Reynolds and Elrick, 1986), tension infiltrometer (Perroux and White, 1988), and single-ring pressure infiltrometer (Reynolds and Elrick, 1990) methods have become very popular and are widely used for measuring K in the field at or near saturation. These methods establish a three-dimensional infiltration process going through an initial transient phase and then approaching steady state.

The most commonly applied approaches for calculating K from three-dimensional infiltration rates measured under both positive (e.g., Guelph permeameter, single-ring pressure infiltrometer) and negative (e.g., tension infiltrometer) values of the pressure head imposed at the infiltration surface use a steady-state flow rate (Wooding, 1968; Reynolds and Elrick, 1987, 1990, 1991; Ankeny et al., 1991). These approaches should be applied to soils that are homogeneous, isotropic, rigid, and at uniform initial water content. In many applications, an infiltration test of relatively short duration is conducted and steady flow is assumed to be attained if the infiltration rate does not vary appreciably with time, or if linearity can be identified on a plot of cumulative infiltration vs. time. However, the estimate of the apparent steady-state infiltration rate can vary with the duration of the experiment (Ankeny et al., 1990; Bagarello et al., 1999; Wu et al., 1999) and it is often questionable to assume that a steady-state condition was reached at the end of a three-dimensional infiltration test (Elrick et al., 1990; Quadri et al., 1994; Vandervaere et al., 2000a). In other words, transient flow data are often analyzed incorrectly by approaches based on flow steadiness. Increasing the duration of the experiment can improve the accuracy of the steady flow estimate, but it can also introduce other inaccuracies given that soil swelling, soil layering, gradients in water content, and changes in soil bulk density are more likely to affect the infiltration measurements as the duration of the experiment and the sampled soil volume increase (Bagarello et al., 1999; Vandervaere et al., 2000a). For these reasons, techniques for analyzing transient flow from single-ring pressure infiltrometers (Wu et al., 1999) and tension infiltrometers (Warrick, 1992; Smettem et al., 1994; Haverkamp et al., 1994; Zhang, 1997; Vandervaere et al., 1997, 2000a, b) have been proposed recently as effective tools for analyzing field data. All the techniques cited above assume that a two-term equation, similar to the one-dimensional Philip's (1957) infiltration equation, can be used, but they differ in the expressions of the two coefficients. In particular, Vandervaere et al. (2000b) used expressions for the two coefficients given by Haverkamp et al. (1994) to determine K from tension infiltrometer measurements by different methods, depending on the number of disk radii and the number of supply pressure head values involved. One of these methods, the TST method, is a transient version of the steady-state method proposed by White et al. (1992).

Vandervaere et al. (2000a) also showed that the choice of the fitting procedure can substantially affect the estimates of the coefficients of the two-term infiltration equation. According to these authors, when a layer of contact material is used for tension infiltrometer experiments, the best method for estimating the two coefficients consists of linearizing the data by differentiating the cumulative infiltration with respect to the square root of time (i.e., differentiated linearization). This method allows a visual check of the validity and range of applicability of the two-term equation.

In some cases, estimating the two coefficients by the DL method can be difficult or even impossible. This happens when the transition time from infiltration into the contact material to infiltration into the soil is difficult to detect because of overlap between the two phenomena (Vandervaere et al., 1997). Minasny and McBratney (2000) applied the DL method to numerically simulated infiltration data and observed that an early-time perturbation, which should be indicative of the wetting phase of the contact material (Vandervaere et al., 2000a), was also detectable when a layer of contact material was not used. Jacques et al. (2002) recently showed that establishing the starting time of infiltration into the soil by the DL method can involve a rather subjective evaluation of the data. It is also necessary to test the time dependence of the coefficients estimated by the DL method, as the estimates of the coefficients of the two-term equation may vary with the duration of the experiment (Haverkamp et al., 1988; Hussen and Warrick, 1993; Clausnitzer et al., 1998).

In this study, field tests of the DL and TST methods were conducted in a sandy loam and a clay soil with the following specific objectives: (i) to identify individual factors that influence the applicability of the DL method by controlling the transition from infiltration into the contact material to infiltration into the soil and (ii) to test the sensitivity of the coefficients of the two-term infiltration equation obtained with the DL method and the sensitivity of the hydraulic conductivity obtained with the TST method to both the duration of the experiment and the time interval between successive readings of the infiltrated water volume.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Transient flow from tension infiltrometers can be described with the following two-term form of the cumulative infiltration equation (Warrick, 1992; Haverkamp et al., 1994; Zhang, 1997):

[1]
where I (L) is the cumulative infiltration, t (T) is the time, and C1 (L T-1/2) and C2 (L T-1) are coefficients related to soil sorptivity and the hydraulic conductivity.

In particular, the following expressions for C1 and C2 were proposed by Haverkamp et al. (1994):

[2]

[3]
where S0 (L T-1/2) is the soil sorptivity corresponding to the negative pressure head, h0 (L), imposed on the soil surface, ß is a constant that can be set equal to 0.6 for practical purposes (Angulo-Jaramillo et al., 2000; Vandervaere et al., 2000b), K0 (L T-1) is the soil hydraulic conductivity at h0, {gamma} is a constant equal to 0.75, r (L) is the disk radius, {theta}0 (L3 L-3) is the volumetric soil water content corresponding to h0, and {theta}i (L3 L-3) is the initial volumetric soil water content. In the infiltration model by Haverkamp et al. (1994), the term S0 corresponds to vertical capillary flow, the term [(2 - ß)/3]K0t corresponds to gravity-driven vertical flow, while the term {{gamma}S20/[r({theta}0 - {theta}i)]}t represents the lateral capillary flow component (Vandervaere et al., 2000b). The dominant term of the flow process can be identified by comparing the soil sorptivity to the Sopt (L T-1/2) parameter (Vandervaere et al., 2000b):

[4]

For a given set of values of r, ({theta}0 - {theta}i), ß, K0, and {gamma}, Sopt is the sorptivity value for which the gravity and lateral capillary terms have equivalent weights in the flow process. If S0 < Sopt, then flow is dominated by gravity and a precise estimation of K0 is possible. If S0 > Sopt, then flow is dominated by lateral capillarity and a precise estimation of K0 is unlikely. If S0 = Sopt, the gravity and lateral capillary terms have equivalent weights in the flow process, and a precise estimation of K0 is possible (Vandervaere et al., 2000b).

Vandervaere et al. (2000b) used Eq. [2] and [3] to estimate K0 from the transient phase of an infiltration experiment (TST method):

[5]

Equation [5] is conceptually similar to the following well-known relationship that uses the steady-state phase of the infiltration experiment for estimating K0 (steady-state, single test, SST, method) (Wooding, 1968; White and Sully, 1987; White et al., 1992):

[6]
where is (L T-1) is the steady-state infiltration rate and b is a constant equal to 0.55 (White and Sully, 1987).

In practice, the coefficients C1 and C2 of Eq. [1] must be estimated using tension infiltrometer data obtained in the field. Determining the coefficients C1 and C2 requires that the validity and range of applicability of the two-term equation be assessed and that the early-time perturbation induced by the layer of contact material placed between the tension infiltrometer membrane and the soil be observed and eliminated. Vandervaere et al. (2000a) recently showed that direct, nonlinear fitting of Eq. [1] on a (I, t) data set (cumulative infiltration, CI, method) offers no check for the adequacy of the form of the two-term equation with the data and may lead to errors in the estimated coefficients that are so large that their values become meaningless even though the perturbation induced by the contact layer seems small and of short duration. Vandervaere et al. (2000a) also suggested that the best technique for determining C1 and C2 consists of linearizing the data by differentiating the cumulative infiltration with respect to the square root of time (DL method):

[7]
where dI/d is approximated by

[8]
where n is the number of data points and the corresponding on the right-hand side of Eq. [7] is calculated as the geometric mean:

[9]

Plots of {Delta}I/{Delta} vs. should be linear, with C1 equal to the intercept and C2 equal to one-half of the slope. If the data set is not linear, Eq. [1] must be considered inappropriate. The influence of the contact material is easy to detect since it corresponds to the initial sharply decreasing part of the curve, deviating from the monotonically increasing linear behavior. Linear regression can then be restricted to the rest of the data set, thus providing values of C1 and C2 without bias (Vandervaere et al., 2000a).


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Two sites were selected to conduct tension infiltrometer experiments in the field (Fig. 1). Table 1 gives the name and location of the field sites, the name and taxonomy of the soils (Soil Survey Staff, 1998), and the particle-size distributions of the soils (Gee and Bauder, 1986). The measurements were conducted with a tension infiltrometer manufactured by Soil Measurement Systems (Tucson, AZ).1 In the sandy loam soil (Palermo), 18 infiltration experiments were performed within a 150-m2 flat area supporting a citrus orchard. In the clay soil (Sparacia), six infiltration experiments were performed within a 176-m2 bare area on a generally uniform 16% slope, choosing small, flat areas for placing the instrument. The soil structure was classified as stable for the sandy loam soil (Bagarello et al., 2000), and unstable (cracking) for the clay soil (Bagarello et al., 2001a). The clay soil appeared massive in the winter when the soil was wet and in fully swelled status, but developed a polygonal pattern of surface shrinkage cracks in late spring or early summer as the soil dried. The sandy loam soil had a gravel content of 16.4% by weight, while the clay soil had a negligible gravel content.



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  		Fig. 1. Location of the experiment sites.

 

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  		Table 1. Selected field site information.

 
In the sandy loam soil, eight long-duration experiments were conducted during the fall of 1998, five short-duration experiments in May 1999 and five additional long-duration experiments in June 1999. The long-duration experiments were between 208 and 226 min long, with one experiment having a duration of 120 min. The short-duration experiments lasted 40 min. Six experiments of duration ranging between 48 and 84 min were conducted in the clay soil in October 2001, before occurrence of rainy periods. At each randomly selected location, a retaining ring having a radius of 120 mm and a nylon guard cloth with an air-entry value ha = -160 mm were placed on the soil surface. A leveled contact layer with a thickness of 10 mm was prepared by using air-dry Spheriglass (Potters Industries, Valley Forge, PA) no. 2227 glass spheres (Reynolds and Zebchuk, 1996; Bagarello et al., 2001b). In the sandy loam soil, a pressure head of -130 mm, for the long-duration experiments, and -60 mm, for the short-duration ones, was established on the infiltrometer membrane to obtain pressure heads, h0, of -120 and -50 mm, respectively, at the soil surface. A value of h0 = -100 mm was used in the clay soil. Water level readings were visually collected at 15- to 30-s intervals for the first 2 min, and then at time intervals increasing from 1 min up to 4 to 16 min.

The duration of the experiments was substantially longer than the duration of the experiments reported in Vandervaere et al. (1997)( 2000a) and the minimum duration suggested by Vandervaere et al. (2000b) for a transient flow data analysis (3–5 min, plus the perturbation by the contact layer). According to Vandervaere et al. (2000b), the transient flow analysis is compatible with situations where steady-state methods are used. In these cases, infiltration data must be collected for a relatively long time in an attempt to measure steady-state infiltration rates. The validity and range of applicability of the two-parameter transient flow equation can then be evaluated by plotting the data in the form of Eq. [7].

For each experiment, data were plotted on a {Delta}I/{Delta} vs. plot to test the applicability of the DL method and to estimate the coefficients C1 and C2 by simple linear regression analysis. The dominant term of the flow was evaluated by comparing the coefficient C1 to the corresponding value of the Sopt parameter (Vandervaere et al., 2000b). Equation [5] was used to estimate K0. Since soil water content was not measured systematically, two extreme values of {Delta}{theta} = {theta}0 - {theta}i ({Delta}{theta} = 0.1 and 0.4 m3 m-3) were considered to calculate Sopt. An estimate of the apparent steady-state infiltration rate, is (L T-1), was also obtained by the slope of the linear part of the cumulative infiltration vs. time curve (Ankeny et al., 1991). The time to apparent steady state, ts (T), was calculated by the following equation (Bagarello et al., 1999):


[10]
where I is the measured cumulative infiltration at time t, Ireg is the regression-based estimate of I at time t, and E is a criterion for establishing the onset of linearity in I vs. t. A restrictive criterion value for E in Eq. [10] equal to 1% was used to estimate ts. The K0 values obtained by Eq. [5] and [6] were then compared by considering two values of {Delta}{theta} ({Delta}{theta} = 0.1 and 0.4 m3 m-3). The estimate of S0 obtained by the DL method was used in Eq. [6] (Vandervaere et al., 2000b).

The dependence of the coefficients C1 and C2 estimated by the DL method and of the values of K0 calculated by Eq. [5] on the duration of the experiment was studied by eliminating progressively an (I, t) measurement from the data set and then repeating the linear regression on the remaining {Delta}I/{Delta} vs. data. Two values of {Delta}{theta} ({Delta}{theta} = 0.1 and 0.4 m3 m-3) were considered for calculating K0 by the TST method. The experimental {Delta}I/{Delta} vs. data obtained from Fig. 7c and 8c of Vandervaere et al. (1997) and Fig. 5 (for the three-dimensional infiltration experiment) of Vandervaere et al. (2000a) were also used for this analysis. Those regressions producing meaningless results (i.e., a negative value of C1, C2, or K0) or coefficients of determination not significantly greater than zero according to a one-tailed t-test (probability level, P = 0.05) were neglected in the analysis.

Sensitivity of C1, C2, and K0 to the time interval between successive readings of cumulative infiltration was also tested. A maximum value of the mean time interval between readings, µ({Delta}t), of 30 min was considered. Quite large values of µ({Delta}t) were considered because reducing the frequency of readings during an experiment simplifies field data acquisition, when the water level is read visually, and allows simultaneous application of several instruments. For each data set, the DL method was applied to estimate C1 and C2, and the TST method was used to calculate K0 for the selected values of {Delta}{theta} ({Delta}{theta} = 0.1 and 0.4 m3 m-3).


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
An abrupt change in slope between the sharply decreasing, early portion of the {Delta}I/{Delta} vs. data set, indicating the influence of the contact material, and the linearly increasing, undisturbed rest of the data set was observed for nine experiments, three of which are shown in Fig. 2. In the other 15 cases, including the longest experiment, a more or less prolonged transition zone was observed between the decreasing and increasing portions of the data set. Two examples of these last experiments are shown in Fig. 3. The presence of the transition zone did not allow a clear selection of the part of the experiment to be used in the fitting procedure. In some cases, however, the initial part of the linearly increasing data set was estimable by enlarging the y scale of the plot.





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  		Fig. 2. Application of the differentiated linearization (DL) method to the field data obtained in Exp. (a) 5L, (b) 8L, and (c) 6TI. The straight line was obtained by regression of the increasing linear part of the {Delta}I/{Delta} vs. data.

 



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  		Fig. 3. Application of the differentiated linearization (DL) method to the field data obtained in Exp. (a) 13L and (b) 2TI.

 
Attempting to individuate the reasons for the limited applicability of the DL method, data from each of the 24 experiments were also plotted on an I vs. plot to visually select the wetting phase of the contact material and the phase where sorptivity of the soil dominates the flow (Cook and Broeren, 1994). Separating the wetting phase of the contact material from the early-time infiltration into the soil was more difficult on a {Delta}I/{Delta} vs. plot (Fig. 3) than on an I vs. plot (Fig. 4). An estimate of the sorptivity of both the contact material (Smc) and the soil (S0) was obtained from the slope of the straight lines interpolating the two groups of I vs. data. The overestimation of S0 that occurs when the I vs. data are used (Smettem et al., 1995; Vandervaere et al., 2000b) was considered negligible in this study. The arithmetic mean value of Smc was 0.421 mm s-1/2 and the corresponding coefficient of variation was equal to 0.35, suggesting that a reasonably uniform contact material was used in the field. In general, the ratios Smc/S0 calculated for the experiments showing an abrupt change in slope between the two portions of the data set were higher than those calculated for the experiments exhibiting a transition zone. In particular, for the nine experiments clearly allowing application of the DL method, Smc/S0 ranged between 10.2 and 56.7 (mean = 24.0). For the 15 experiments showing a transition zone between the decreasing and increasing portions of the data set, Smc/S0 was in the range 1.9 to 12.3 (mean = 6.5). It appears therefore that a clear discontinuity in Fig. 2 between the sharply decreasing, early portion of the data set and the linearly increasing behavior for the rest of the data set was detectable when the capillary forces of the contact material were much higher than the soil capillary forces. As the differences in capillary forces between the contact material and soil decreased, a transition zone, complicating or impeding the application of the DL method, appeared between the two parts of the data set. An interesting strategy to obtain an abrupt change in slope between the decreasing early portion of the {Delta}I/{Delta} vs. data set and the linearly increasing undisturbed rest of the data set could consist of using initially dry contact material on relatively wet soil.




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  		Fig. 4. Cumulative infiltration, I, vs. square root of time, , for Exp. (a) 13L and (b) 2TI. The straight lines are the regressions of I vs. for the contact material wetting phase (dotted line) and for the phase where sorptivity of the soil dominates the flow (continuous line).

 
The experiments clearly showing applicability of the DL method (N = 9), were used for further analysis (Table 2). For each experiment, the linearity of the monotonically increasing part of the {Delta}I/{Delta} vs. data set was observed visually (Fig. 2) after Vandervaere et al. (2000a), and further confirmed by the statistical significance (P = 0.05) of the coefficients of determination, r2. The maximum value of the ratio between C1 and Sopt was equal to 0.39, suggesting that an accurate estimation of K0 was expected for these experiments (Vandervaere et al., 2000b). The two soils considered in this investigation were situated in the domain of gravity as the real soils investigated by Smettem et al. (1998).


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  		Table 2. Hydraulic conductivity, K0, values obtained at the two field sites by the transient single-test (TST) and steady-state single-test (SST) methods for two values of the difference, {Delta}{theta}, between the water content corresponding to the imposed pressure head, {theta}0, and the initial water content, {theta}i. The coefficients C1 and C2 of the two-parameter infiltration equation, the steady-state infiltration rate, is, the time to steady state, ts, and the Sopt parameter are also listed.

 
Examining the infiltration data on an I vs. t plot showed that a linear portion of the experimental (I, t) data pairs was clearly detectable some time after the initiation of the infiltration process (Fig. 5). For each experiment, a very convincing, apparent steady-state infiltration rate, is, was obtained, and the time to apparent steady state, ts, was also clearly determined (Table 2). Therefore, the same data set appeared analyzable both by using steady-state flow solutions and by approaches developed for transient stages only. The estimates of K0 obtained by the steady-state approach were lower than the corresponding estimates obtained by the transient flow analysis, and the ratio between the two values of K0 ranged from 0.4 to 0.8 (Table 2). Therefore, the method of analysis of a given data set is one of the numerous sources of variability of the hydraulic conductivity estimates. Independently of the method of analysis (transient, steady), the geometric mean values of K0 obtained at the two sites (Table 2) were relatively similar, differing by a maximum factor of approximately three. This result suggested that soil macroporosity at the time of the experiments was an important factor affecting the K0 results obtained in the clay soil.



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  		Fig. 5. Cumulative infiltration, I, vs. time, t, for Exp. 5L. The straight line was obtained by regression of the linear part of the I vs. t data.

 
The coefficients C1 and C2 estimated with the DL method and the hydraulic conductivity calculated with the TST method varied with both the duration of the experiment (Table 3) and the time interval between successive readings at the instrument reservoir (Table 4).


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  		Table 3. Minimum and maximum values of the coefficients C1 and C2 obtained with the differentiated linearization (DL) method by considering different durations of the tension infiltrometer experiment and of the corresponding hydraulic conductivity, K0, calculated with the transient single-test (TST) method for two values of {Delta}{theta}. For each variable, the percentage difference between the maximum and the minimum value is given in parenthesis.

 

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  		Table 4. Minimum and maximum values of the coefficients C1 and C2 obtained with the differentiated linearization (DL) method by considering different time intervals, {Delta}t, between successive water level readings at the instrument reservoir and of the corresponding hydraulic conductivity, K0, calculated with the transient single-test (TST) method for two values of {Delta}{theta}. For each variable, the percentage difference between the maximum and the minimum value is given in parenthesis.

 
For the experiments conducted in this study, the minimum number of points to be included in the regression between {Delta}I/{Delta} and to obtain meaningful and statistically significant results varied between 5 and 12, depending on the experiment, with two exceptions (Exp. 8L and 11L, with a minimum number of points equal to 3 and 4, respectively). The difference, {Delta}C1, between the maximum and the minimum values of C1 obtained by considering different durations (Table 3) varied between 28.4 and 15000%, depending on the experiment. The difference calculated for the coefficient C2 ({Delta}C2) ranged between 17.0 and 445.9%. For K0, the variable of main practical interest, the difference, {Delta}K0, varied between 17.2 and 37.1% for most experiments (Exp. 12L, 2S, 4TI, 5TI, and 6TI). It was approximately equal to 55% for Exp. 11L, and it ranged between 107.3 and 657.8% for a few experiments (Exp. 5L, 8L, and 1TI). A very noticeable time dependence of C1, C2, and K0 was observed for Exp. 8L (Table 3). A close examination of the {Delta}I/{Delta} vs. plot for this last experiment showed that a monotonically increasing behavior was observed for either the whole experiment duration and times <479 s (Fig. 2b). Considering the data points corresponding to t < 479 s, the fitted coefficients were C1 = 2.02 x 10-4 mm s-1/2 and C2 = 1.14 x 10-3 mm s-1 (r2 = 0.99999; sample size, N = 5) and these values were very different from those obtained by considering all data (Table 2). Considering an additional data point (N = 6) produced a coefficient of determination for the regression not statistically different from zero (r2 = 0.0026).

The time dependence of the K0 estimates was appreciable for only three experiments (Exp, 5L, 8L, and 1TI), given that an error of the estimate of K0 by a factor of two can be considered small for many practical purposes (Elrick and Reynolds, 1992). A thorough evaluation of the combined effect of the duration of the experiment and the soil type on the K0 results was not possible because the number of experiments successfully analyzed with the DL method was low (five at Palermo and four at Sparacia). We note, however, that a higher frequency of high {Delta}K0 values was obtained at Palermo. Experiments of similar duration conducted at a given site, and resulting in relatively similar estimates of K0 (Table 2), produced both high (i.e., >100%) and low values of {Delta}K0 (Table 3). For the long-duration experiments conducted at Palermo, {Delta}K0 decreased as the minimum duration considered for calculating C1 and C2 increased. This trend was not observed for the experiments conducted at Sparacia that were characterized by similar values of the minimum duration. Therefore, the time dependence of the K0 estimates was more appreciable for the long-duration experiments conducted in the sandy loam soil than for the relatively short-duration experiments conducted in the clay soil, but it was not controlled exclusively by the duration of the experiment.

For the Vandervaere et al. (1997) experiments, the fitted values of C1 were equal to 0.115 m s-1/2 (r2 = 0.7814) for the experiment reported in their Fig. 7c and to 0.075 m s-1/2 (r2 = 0.7666) for the experiment reported in their Fig. 8c. These values were very close to the published values of S0 (=C1), equal to 0.112 and to 0.077 m s-1/2, respectively. Also for the experiments by Vandervaere et al. (1997)(2000a), the C1 and C2 coefficients varied with the duration of the infiltration process (Table 3). Values of {Delta}C1 ranging from 21.3 to 42.8% and of {Delta}C2 ranging from 94.9 to 137.5%, depending on the experiment, were obtained. Therefore, time dependence of the coefficients of the two-term infiltration equation estimated with the DL method was not limited to the experiments conducted in this investigation at the Palermo and Sparacia sites, but it was a more general problem, confirming that it is inherent to the infiltration process.

Varying the time interval between successive readings at the instrument reservoir produced {Delta}C1 values ranging from 13.6 to 941%, {Delta}C2 values varying between 4.2 and 29.4%, and {Delta}K0 values varying between 4.2 and 48.9% (Table 4). Sensitivity of C1, C2, and K0 to the time interval between readings was higher at Sparacia than at Palermo, and C1 was the most sensitive parameter at both sites (Table 4). Both low and very high values of {Delta}C1 were observed at Sparacia for experiments similar in the range of time intervals and the number of data sets considered for the analysis (e.g., Exp. 1TI and 6TI, Table 4).

In general, C1 was much more sensitive than C2 and K0 to both the duration of the experiment and the time interval between readings. This was probably due to the fact that the soils were situated in the domain of gravity (i.e., C1 < Sopt), where the estimation of C1 is made difficult by the importance of the gravity term (Vandervaere et al., 2000b). These estimates of C1 appeared to be unusable in practice given that they depended strongly on the duration of the experiment. In the domain of gravity, however, C1 has little importance in the calculation of K0. This explains why the variability of C1 did not affect appreciably the variability of K0 that was controlled primarily by that of the coefficient C2. Variation of K0 with the time interval between readings was probably negligible for many practical purposes, independently of the soil type and for a very wide range of mean time intervals between readings. The effect of the duration of the experiment on the estimate of K0 was appreciable for three experiments (Exp. 5L, 8L, and 1TI). For these experiments, however, the dependence of the estimates of K0 on the duration of the experiment was particularly strong during the initial part of the experiment (Fig. 6), and it became practically negligible (i.e., 24.0% <= {Delta}K0 <= 39.0%) when a minimum duration of 42 to 96 min, depending on the experiment, was considered in the analysis. In the real soils sampled in this study, conducting experiments of relatively long duration (i.e., approximately an hour or more) is therefore recommended to reduce the risk of obtaining K0 predictions that depend strongly on the duration of the experiment.



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  		Fig. 6. Soil hydraulic conductivity, K0, estimate vs. duration of the experiment.

 

   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
A recently proposed analysis of transient flow from a tension infiltrometer presumably was to overcome several limitations of traditional steady-state methods. The coefficients C1 and C2 of the two-term infiltration equation can be used to estimate the soil hydraulic conductivity, K0, by a TST method that is the transient version of the well-known steady-state, single test method. To obtain reliable estimates of C1 and C2, a DL method may be used. This method consists of differentiating cumulative infiltration, I, with respect to the square root of time, t. The DL method allows one to reveal and eliminate the influence of the contact material at the beginning of the experiment.

In this study, field tests of the DL and TST methods were conducted in a sandy loam and a clay soil. Field experiments were conducted to identify in particular those factors controlling the transition from infiltration into the contact material to infiltration into the soil and to explore sensitivity of the estimates of C1, C2, and K0 to both the duration of the experiment and the time interval between successive readings of cumulative infiltration.

An abrupt change in slope between the sharply decreasing, early portion of the {Delta}I/{Delta} vs. data set, indicating the influence of the contact material, and the linearly increasing part of the data set was observed for about the 40% of the experiments. These experiments were characterized by a ratio between the sorptivity of the contact material (Smc) and of the soil (S0) greater than 10 to 12, and hence, by a relatively high difference in capillary forces between the contact material and the soil. For the remaining experiments, a transition zone between the decreasing and increasing portions of the data set was observed. For these experiments, the ratio between Smc and S0 was lower than 10 to 12, and thus differences in capillary forces were relatively low. The presence of this transition zone can complicate and impede the application of the DL method. A possible strategy to obtain an abrupt change in slope between the decreasing early portion of the {Delta}I/{Delta} vs. data set and the linearly increasing undisturbed rest of the data set consists of using initially dry contact material on relatively wet soil.

The estimates of the soil hydraulic conductivity obtained with the TST method varied with both the duration of the experiment and the time interval between successive readings at the instrument reservoir. Variability of K0 was controlled primarily by variability of C2, while variability of C1, which was much more appreciable than variability of C2, did not have a substantial effect on the estimates of K0. This result was attributed to the fact that both soils were situated in the domain of gravity, where the estimation of C1 is made difficult by the importance of the gravity term, and this coefficient has little importance on the calculation of K0. Independently of the soil type and for a very wide range of mean time intervals between readings (i.e., from a minimum of 1.5 to 9.5 min to a maximum of 8.4 to 28.0 min, depending on the experiment), choosing different intervals between readings produced values of K0 that varied by less than about 50%. This variation is probably not significant compared with other sources of variability for many practical purposes; therefore, it was concluded that the time interval between readings did not affect substantially the estimates of K0. In most cases, choosing different durations of the experiment produced values of K0 that varied by less than 40%. For three experiments, however, K0 varied by up to 650% with the duration of the experiment. The time dependence of the estimates of K0 was more appreciable in the sandy loam soil than in the clay soil and it was not controlled exclusively by the duration of the experiment. The dependence of the estimates of K0 on the duration of the experiment was particularly noticeable during the initial part of the experiment. For the real soils considered in this study, conducting experiments of relatively long duration (i.e., approximately an hour or more) is recommended to reduce the risk of obtaining predictions of K0 that depend strongly on the duration of the experiment.


   ACKNOWLEDGMENTS
 
This study was supported by grants of the Italian Ministero dell'Istruzione, dell'Università e della Ricerca. The authors wish to thank V. Castronovo and G. Tusa for their help in field data collection and J.P. Vandervaere for providing useful comments and suggestions on an earlier version of the manuscript. Both authors set up the experimental activity, examined the results, and concurred in writing the paper.


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




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