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DIVISION S-1—SOIL PHYSICS

A Simplified Falling-Head Technique for Rapid Determination of Field-Saturated Hydraulic Conductivity

^a Dipartimento di Ingegneria e Tecnologie Agro-Forestali, Università degli Studi di Palermo, Viale delle Scienze, 90128, Palermo, Italy
^b Dep. of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada N1G 2W1

^* Corresponding author (bagav{at}unipa.it).

	ABSTRACT

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Simplified measurements of the field-saturated hydraulic conductivity, K_fs, require short duration experiments, small water volumes, and easily transportable equipment. A simplified falling-head (SFH) technique for the rapid determination of K_fs has been developed and tested. The technique consists in applying a small volume of water on a soil surface, confined by a ring inserted a short distance into the soil, and then measuring the time from the application of water to the instant at which the surface area is no longer covered by water. A measurement of the initial and field-saturated soil water contents, and an estimate of the * parameter of the Gardner's exponential model are then used to calculate K_fs using a simple solution that includes gravity. The K_fs of both repacked and undisturbed soil cores was determined in the laboratory by the SFH and the early time constant-head (ECH) techniques. The SFH and (constant-head) pressure infiltrometer (PI) techniques were then compared in the field. The maximum discrepancy between the mean K_fs results obtained within an experiment was of a factor of approximately two. This difference is negligible in most practical applications and it was concluded that the SFH technique compared favorably with the ECH technique in the laboratory and to the PI technique in the field. The SFH technique appears promising for determining K_fs in a relatively short period of time without the need for extensive instrumentation or analytical methodology, and therefore it appears suitable for detailed field measurements over large areas.

Abbreviations: CV, coefficient of variation • ECFH, sequential early time constant head/early time falling head • ECH, early time constant head • EFH, early time falling head • GA, Green and Ampt • K_fs, field-saturated hydraulic conductivity • OPD, one-ponding depth • PI, pressure infiltrometer • SFH, simplified falling head • TPD, two-ponding depth

	INTRODUCTION

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
THE HYDRAULIC CONDUCTIVITY of saturated soil is one of the most important soil properties controlling water infiltration and surface runoff, leaching of pesticides from agricultural lands, and migration of pollutants from contaminated sites to the ground water.

Saturated hydraulic conductivity depends strongly on soil texture and structure, and therefore can vary widely in space. Since hydraulic conductivity is determined essentially at points on a field scale, a large number of determinations is required to assess the magnitude and structure of the variation within the selected area (Logsdon and Jaynes, 1996). Spatially distributed determinations of hydraulic conductivity have to be repeated at different times, particularly in soils where structure varies over time because of natural or anthropogenic factors (Prieksat et al., 1994). For structured soils in particular, saturated hydraulic conductivity has to be measured directly in the field to minimize disturbance of the sampled soil volume and to maintain its functional connection with the surrounding soil (Bouma, 1982). Using small volumes of water, easily transportable equipment, and conducting short-duration experiments is desirable to obtain K_fs data at a great number of locations over a large area and with the realistic use of resources in terms of time and costs.

Most field techniques, such as the traditional well permeameter and ring infiltrometer constant-head techniques (Reynolds and Elrick, 1986, 1990), rely on the attainment of a steady-state flow rate of water into the soil (Elrick and Reynolds, 1992b; Reynolds, 1993), and this can limit their field use since short-duration steady-state experiments can be conducted only in relatively permeable soils (Elrick and Reynolds, 1992a). Other studies have shown, however, that short duration experiments can also be conducted in low permeability soils using early time transient flow measurements from a surface ring to obtain estimates of K_fs (Fallow et al., 1994; Elrick et al., 1995; Odell et al., 1998). The simplest technique that uses the initial period of the infiltration process to deduce K_fs is probably the ECH technique. This technique was specifically developed for short-time measurements of the saturated hydraulic conductivity of very low permeability soils (i.e., K_fs < 1 x 10^–9 ms^–1) (Fallow et al., 1994; Odell et al., 1998). For both steady-state and ECH infiltration experiments, a constant head device has to be used, and transported throughout the area of measurement. Using a falling-head experiment to determine K_fs in situ is preferable since this type of experiment is simpler than a constant-head experiment (Philip, 1992). This approach has been used recently for determining K_fs from borehole measurements (Munoz-Carpena et al., 2002).

Using previous work conducted by Smith (1999) and Elrick et al. (2002), we developed a SFH technique for measuring K_fs. Field application of this technique requires only a small ring that is inserted to a short distance into the soil, a small volume of water, and a stopwatch. In this paper, the simplified method for measuring K_fs is presented and a laboratory and a field evaluation of its performance is performed.

	A Review of Some Transient Flow Equations and Their Applications

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The initial flow of water from a surface ring into initially unsaturated soil is controlled almost solely by the pressure head and capillary sorption and it can be considered to be one-dimensional and free from gravitational effects so that the cumulative infiltration of water, I (L), can be described by (Philip, 1957, 1969):

[1]

where S_H (L T^–1/2) is the soil sorptivity for a ponded head, H (L), and t (T) is the time.

During constant-head conditions, S_H is invariant and it can be expressed by the following approximate analytical relationship, that was deduced using previous work by White and Sully (1987) (Fallow et al., 1994):

[2]

where is the difference between the field-saturated water content, _fs (L³ L^–3), and the initial water content, _i (L³ L^–3), _m (L² T^–1) is the field-saturated matric flux potential, b is a constant equal to 0.55 (White and Sully, 1987), and K_fs (L T^–1) is the field-saturated hydraulic conductivity. The first term in Eq. [2] gives the sorptivity, S₀, for H = 0 and the second term gives the increase in sorptivity due to the positive (ponded) head, H. The Green and Ampt (1911) (GA) equation can also be used to derive another approximate expression of S_H for constant-head conditions:

[3]

where _f (L) is the soil water pressure head at the wetting front, and _f is negative. Since, for rectangular hydraulic conductivity function like GA, _m and _f are related by (Elrick et al., 2002):

[4]

the only difference between Eq. [2] and [3] is in the estimation of b that is equal to 0.5 for GA soils. Solving Eq. [2] for K_fs gives:

[5]

and solving Eq. [3] for K_fs gives:

[6]

where the * parameter (L^–1) is given by (Elrick and Reynolds, 1992a):

[7]

Equations [5] and [6] can be used for determining K_fs from early time flow data under a constant head (Fallow et al., 1994; Odell et al., 1998; Elrick et al., 1995, 2002). The procedure, the ECH technique by Fallow et al. (1994), evaluates S_H from the slope of the linear portion of the I vs. t^1/2 graph, and needs the measurement of and the estimation of the * parameter (Elrick and Reynolds, 1992b).

During early time falling head (EFH) infiltration, S_H is variable and therefore does not exhibit a linear behavior on a graph of I vs. t^1/2 (Odell et al., 1998). For falling-head conditions, the cumulative infiltration is a function of H as follows (Elrick et al., 1995):

[8]

where a (L²) is the cross-sectional area of the falling-head tube, A (L²) is the cross-sectional area of the infiltrating surface and H₀ (L) is the height of the ponded head at t = 0. Fallow et al. (1994) used Eq. [2] to approximate a falling-head infiltration process based on a succession of constant-head conditions:

[9]

where the impact of the falling head is given by the term H(t). Substitution of Eq. [8] into Eq. [9] yields (Fallow et al., 1994; Elrick et al., 1995):

[10]

Equation [10] was fitted to EFH data by a nonlinear, least-squares procedure to determine simultaneously K_fs and _m (EFH technique) (Fallow et al., 1994). Since H₀ was difficult to obtain, the EFH technique was later extended by Elrick et al. (1995) by the addition of an initial period of constant-head infiltration at H = H₀ (Sequential Early-Time Constant-Head/Falling-Head [ECFH] technique). Recently, Elrick et al. (2002) used the GA approach to deduce a new implicit equation in I for falling-head conditions that neglects gravity:

[11]

where:

[12]

The GA expression for a falling head that includes gravity was derived by Philip (1992):

[13]

where:

[14]

Equations [11] and [13] are valid until the falling head drops to zero.

To evaluate the applicability of early time techniques, the accuracy of the K_fs determination has to be established by also distinguishing between early time techniques requiring an independent estimation of * (ECH technique) and early time techniques allowing simultaneous determination of K_fs and _m or * (EFH and ECFH techniques). See Elrick and Reynolds (1992b) for a discussion of the two procedures referred to above as applied to the constant-head permeameter. Only a few investigations have been conducted to evaluate the reliability of the estimates of K_fs and _m (or *) obtained from early time ponded flow experiments and most investigations have used the solutions deduced from Eq. [2] (Vauclin et al., 1994; Elrick et al., 1995; Odell et al., 1998).

It has been well established that field-saturated hydraulic conductivity tends to be obtained more reliably than * from steady, ponded flow out of a ring since the hydrostatic pressure and gravity components of flow are maximized rather than the capillary component (Reynolds and Elrick, 1990; Vauclin et al., 1994; Elrick et al., 1995; Bagarello et al., 2000; Mertens et al., 2002). Also, * is obtained from K_fs/_m and thus contains the variability in the calculation of both K_fs and _m. The estimates of K_fs appear more stable than those of * (Elrick et al., 2002) and not greatly affected by the early time technique used (Odell et al., 1998), suggesting that early time ponded flow experiments can be used to estimate K_fs. In this sense, a simplified approach with a priori estimate of the * parameter appears more attractive than a more complicated approach involving additional loads of an experimental and computational nature.

	The Simplified Falling-Head Technique

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The SFH technique consists in applying quickly a small volume of water, V (L³), on the soil surface confined by a ring (a/A = 1) inserted to some distance into the soil and in measuring the time, t_a (T), from the application of water to the instant at which the surface area is no longer covered by water. At t = t_a, I(t_a) = H₀ = D, where D = V/A (L) is the depth of water corresponding to V. Equation [13], with Eq. [7] inserted, then becomes:

[15]

Estimation of K_fs by Eq. [15] requires measurement of both t_a and and the estimation of the * parameter. No theoretical limitations exist on the area to be sampled, but there are practical limitations. Knowledge of and of the depth of insertion of the ring into the soil allows the investigator to determine the volume of voids within the soil volume confined by the ring. A volume of water less than or equal to the volume of voids can then be selected to assure one-dimensional flow during the experiment. Equation [15] is precisely Eq. [5] of Philip (1992) solved for K_fs. Since Eq. [15] includes gravity, the only time limitation will occur if the wetting front emerges from the bottom of the ring and three-dimensional flow commences.

For three K_fs–* combinations (K_fs = 1 x 10^–4 m s^–1 and * = 36 m^–1; K_fs = 1 x 10^–6 m s^–1 and * = 12 m^–1; K_fs = 1 x 10^–8 m s^–1 and * = 4 m^–1) and two values of ( = 0.2 m³m^–3 and = 0.4 m³m^–3), Figure 1 shows the relationship between t_a and D according to Eq. [15]. For illustrative purposes, D was allowed to vary between 0.005 and 0.03 m (for = 0.2 m³ m^–3) or 0.06 m (for = 0.4 m³ m^–3). These maximum values of D correspond to the volume of water required to fill the initially air-filled voids in the soil volume confined by the ring. An insertion depth of 0.15 m was considered since it appears to be a reasonable compromise between the need of avoiding excessive disturbance of the sampled soil volume and that of assuring one-dimensional flow. For K_fs = 1 x 10^–4 m s^–1, t_a is generally <5 min while t_a is >3.5 h for K_fs = 1 x 10^–8 m s^–1. It appears, therefore, that falling-head experiments of reasonable duration can potentially be conducted on a broad range of soils. In particular, the SFH experiment appears more attractive than the traditional constant-head field techniques for determining the field-saturated conductivity of relatively low permeability soils. The traditional methods typically rely on the attainment of a steady-state flow rate that can take several days to occur (Odell et al., 1998). The same falling-head experiment can be also used to determine soil sorptivity if gravity effects are negligible (Smith, 1999).

View larger version (20K): [in this window] [in a new window]   Fig. 1. Relationship between the duration of the falling-head experiment, ta, and the initial depth of water, D, established on the infiltration surface, for different values of the field-saturated hydraulic conductivity, Kfs, the * parameter, and the difference between the field-saturated and the initial water content, .

[16]

where K_fs(ß_p) is the K_fs value obtained by perturbing one of the input data while maintaining the others constant. A variation of ±10% of the true value was considered for D, , and t_a. A variation of plus or minus one category among those proposed by Elrick and Reynolds (1992a) was considered for the * parameter; for example, 12 m^–1 was replaced by 4 m^–1. The values of e_K ranged from –9.0 to +11.0% for both and t_a. Values of e_K ranging from –19.0 to +21.0% and from –74.0 to +179.0% were obtained for D and *, respectively.

Sensitivity of K_fs to minor changes in D, , and t_a was small and probably negligible in practice, given that K_fs varies over several orders of magnitude in nature. An implication of this result was that in most cases the determination of K_fs should not be greatly affected by the assumption that the infiltration surface was smooth or by small errors (i.e., ±10% of the true value) in the measurement of the soil water content or the duration of the infiltration process. Moreover, the assumption that the initial depth of ponding was established instantaneously on the infiltration surface appeared to be generally reasonable. An improper evaluation of * by one category yielded a K_fs value differing appreciably from the true value. Similar levels of error have been reported for steady-state experiments conducted with the Guelph permeameter and PI techniques (Reynolds and Elrick, 1990; Elrick and Reynolds, 1992a; Bosch, 1997) and they have been considered acceptable for many practical applications (Elrick and Reynolds, 1992a). Moreover, an erroneous choice of * appears rather unlikely, given that only four categories were suggested by Elrick and Reynolds (1992a) for describing a very wide range of soils.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Laboratory Experiments
Experiments were conducted on both undisturbed soil cores and packed soil columns to compare the hydraulic conductivity values obtained by the ECH and SFH techniques. These techniques show similarities since both use the initial portion of the infiltration process, need an estimate of the * parameter and sample small and relatively similar soil volumes.

Nine undisturbed soil cores having a silty clay loam texture (Soil Survey Staff, 1998) were collected in 0.085-m diam. x 0.11-m high stainless steel cylinders from the upper layer of a soil classified as Chromic Calcixerert (Soil Survey Staff, 1998), after eliminating the first 0.02 to 0.03 m of soil. Each cylinder was inserted vertically into the soil by hammering gently on the top of the cylinder with a rubber hammer and progressively removing the surrounding soil up to the established depth to reduce disturbance during sampling. The height of the soil cores varied between 0.055 and 0.092 m with a mean value of 0.072 m. In the laboratory, a nylon filter and a rigid wire screen were connected to the base of the core to prevent soil loss from the bottom of the sample and the cores were weighed to determine the initial soil water content. A small depth of water, D = 0.015 m, was then applied on the soil surface and the time, t_a, from the application of water to the instant at which the surface area was no longer covered by water was measured. Depending on the soil core, t_a varied between 141 and 9914 s, with a mean value of 1575 s. For all but two experiments (cores C4 and C7, having a volume of air-filled voids of 75.5 and 79.8 cm³, respectively), the infiltrated volume of water (V = 85.1 cm³) was less than the volume of air-filled voids at the time of the experiment. Soil cores were then exposed to air in the laboratory to promote loss of water. After about 10 d, the cores were weighed again and a constant head of water, H, of 0.014 m was established on the soil surface. Early time infiltration data were collected during the first 679 to 14413 s (mean = 2645 s) and they were used to obtain an estimate of S_H. Starting from the collection time, separation of the soil from the cylinder wall was never observed for these undisturbed cores. The soil cores were then oven-dried and weighed. For each soil core, two estimates of the K_fs were obtained. In particular, a value of K_fs was obtained from the SFH experiment, using Eq. [15], and another value of K_fs was obtained from the ECH experiment, using Eq. [6]. To maintain simplicity of the tested early time methods, the field-saturated soil water content was assumed to be equal to total porosity that was calculated from dry bulk density measurements. A value of * = 12 m^–1 was used to calculate K_fs (Elrick and Reynolds, 1992a, b).

Laboratory experiments were also conducted to determine the K_fs of a compacted artificial soil composed by equal weights of a mono-granular sand (particle diameter, d_p = 73 µm) and a commercial kaolin powder (median diameter d₅₀ = 3 µm). This mixture was chosen since preliminary tests showed its ability to provide values of K_fs that were reasonably low for the purposes of the investigation and from cores that did not swell appreciably on wetting. Forty-two 0.05-m diam. by 0.04- or 0.05-m high columns having a mean bulk density of 1.38 g cm^–3 (coefficient of variation [CV] = 1.6%) were prepared by using the air-dried mixture. A step-by-step procedure was applied to prepare the core. At each step, a fixed amount of artificial soil, corresponding to a height of the core of about 0.01 m, was put in the cylinder and then it was manually compacted. Efforts were made to give similar amounts of compacting energy to each layer. The SFH technique was used to determine the K_fs of 22 cores. A depth of water, D = 0.01 m, was used for these experiments. Depending on the core, t_a varied between 442 and 2841 s, with a mean value of 1301 s. The ECH technique was applied to determine the K_fs of 20 cores. A constant depth of ponding, equal to 0.01 m, was maintained to determine S_H from early time infiltration measurements that were collected for the initial 133 to 347 s (mean = 270.2 s), depending on the experiment. Equation [6] was used to calculate K_fs. For both techniques (SFH, ECH), _i was set equal to the mean of the measured values for the air-dried material (_i = 0.03 m³m^–3) and _fs was estimated from bulk density measurements. The mean depth of the wetted layer was calculated to be equal to 0.022 m for the SFH experiments and to 0.010 m for the ECH experiments. Published values of * were not available for the artificial soil used in the repacked soil experiments. Therefore, to establish the value of * to be used in the calculations, the wetting retention curve of three replicated soil columns was determined in the pressure head range –1200 h –10 mm. The Brooks and Corey (1964) equation was then fitted to the water retention data by using the RETC code (van Genuchten et al., 1991) and an estimate of * was obtained from (Fallow et al., 1994):

[17]

where h is the pressure head, h_i is the initial (negative) pressure head, S_e = ( – _r)/(_s – _r) is the effective saturation, _s and _r are the saturated and the residual water content, respectively, is a pore-connectivity parameter, set equal to 0.5 (Mualem, 1976), and is the exponent of the Brooks and Corey (1964) equation. A value of * equal to 2.0 m^–1 was obtained and used in the calculations.

Each set of K_fs values was summarized by calculating the mean and the CV of the individual measurements. The statistical frequency distributions for the K_fs data obtained from the undisturbed soil core experiments were found to be log-normal (data not shown), which is common for undisturbed soil (e.g., Lee et al., 1985; Warrick, 1998). Geometric means and the associated coefficients of variation were therefore calculated (Lee et al., 1985). The statistical frequency distributions for the K_fs data obtained from the repacked soil cores were found to be normally distributed (data not shown). This result was expected since unstructured soil was used for these experiments. Arithmetic means and the associated coefficients of variation were therefore determined.

Field Experiment
Field experiments were conducted to compare the SFH technique with the PI (Reynolds and Elrick, 1990) technique for measuring K_fs. Reasons for choosing this last technique for the comparison include: (i) the PI technique is one of the simplest techniques for measuring K_fs in the field, (ii) it appears to yield K_fs results that are comparable with other techniques (e.g., tension infiltrometer, laboratory soil cores) for different soil type and land management combinations (Reynolds et al., 2000), and (iii) the same surface area can be sampled with the SFH and PI techniques and this should simplify the interpretation of the K_fs results.

The field site is located near Menfi (western Sicily, Italy), approximately 90 km south of Palermo, at an altitude of 20 m above sea level. The field is flat and supports a 2-yr-old espalier system vineyard (Vitis vinifera) with a distance between the rows of vines of 2.20 m. The soil is classified as Chromic Calcixerert (Soil Survey Staff, 1998). An area of approximately 40 by 4.40 m² was chosen for the investigation and 30 sites were randomly selected within this area. Soil texture of the 0- to 0.05- and 0.05- to 0.10-m layers was determined on 30 soil samples collected in the vicinity of each site (Table 1). The soil was classified as loam (Soil Survey Staff, 1998) in most cases (87% of the total) and sandy clay loam or sandy loam in a few cases (8 and 5% of the total, respectively). The gravel content was negligible.

At each site, an experiment with the SFH technique was conducted both before and after the PI experiment to also test the effect of the sequence of the experiments on the K_fs results. Different authors have shown that repeating an infiltration experiment on the same soil core can have an appreciable influence on the K_fs results (Bagarello et al., 2000; McKenzie et al., 2001). The first SFH experiment was conducted immediately after ring insertion and the PI experiment was performed 10 to 37 d after the SFH experiment. Eight to 30 d after the PI application, 15 L of water were poured on each bounded area, including the surface area confined by the ring, to reduce differences between the water content of the soil volume confined by the ring and that of the soil surrounding the ring. The second SFH experiment was conducted on 1 Oct. 2002, 20 d after this last wetting. A total rain amount of 18.2 mm was registered during the experimental period. Most of this rain (i.e., 14.4 mm) occurred after the PI application. The daily temperature varied between 17.5 and 31.0°C, with a mean value of 23.7°C.

For the SFH experiments, a pre-established volume of water was applied on the soil surface in a few seconds (i.e., approximately 5 s) and the time t_a from the application of water to the instant at which the surface area was no longer covered by water was measured. For comparative purposes, the time, t_0.5a, at which half the surface area was no longer covered by water was also recorded. Two undisturbed soil cores (0.05-m diam. by 0.05-m high) were collected within the bounded area at a depth of 0 to 0.05 and 0.05 to 0.10 m, respectively, before each SFH experiment. These cores were used to determine the bulk density and the initial volumetric soil water content that were averaged over the two depths. Field-saturated water content was calculated using bulk density results. Before conducting each SFH experiment (as well as each PI experiment), the soil surface confined by the ring was gently moved with a spatula to remove any surface crust and to improve the contact between the soil and the inside wall of the ring. A site-specific determination of was not obtained before each experiment. A constant value of V (V = 429.4 cm³, 0.025 D 0.030 m, depending on the ring), giving one-dimensional flow for 0.25 m³ m^–3, was used for all the SFH experiments. One-dimensional flow was however checked after the SFH experiment. The depth of the wetting front, d_w (L), at the end of the SFH experiment was calculated by the following relationship:

[18]

and it was <0.12 m in all but two cases (d_w = 0.121 and 0.138 m, respectively). The mean value of d_w was equal to 0.088 m (standard deviation, = 0.018 m) for the first set of SFH experiments and 0.080 m ( = 0.016 m) for the second set of SFH experiments. Equation [15] was used to calculate K_fs for each SFH experiment. According to Elrick and Reynolds (1992a), a value of the * parameter equal to 12 m^–1 was used for the calculations.

The PI experiments were conducted by using two infiltrometers consisting of a Mariotte reservoir 1.0-m high with an inner diameter of 0.11 m. Two pressure heads were established on the soil in succession and in ascending order (H₁ = 0.05 m, H₂ = 0.107 m). After some preliminary tests, the duration of the experiment was set to 4 h for the first pressure head and to 3 h for the second pressure head. This duration allowed us to obtain apparent steady-state conditions for both steps of each experiment. For one site only, a unique ponding head (H = 0.05 m) was used because the infiltration process was particularly slow and the duration of the experiment exceeded 11 h. The rate of fall of the water level in the infiltrometer reservoir was monitored at 2- to 5-min time intervals. In many cases, high infiltration rates were observed and the water reservoir emptied before concluding the experiment. Refilling of the reservoir was conducted by maintaining ponded conditions on the soil surface confined by the ring. Apparent steady state was detected on a flow rate versus time plot. Flow at the end of the first step of the experiment was three-dimensional because the volume of water discharged from the PI reservoir was greater than the volume of the initially air-filled voids in the soil volume confined by the ring (a dry initial condition, i.e., = 0.4 m³m^–3, was assumed for these calculations) plus the volume of water required to maintain H₁ = 0.05 m above the soil surface. The three-dimensional flow is taken into account by the PI equation. Both the two-ponding depth (TPD) and the one-ponding depth (OPD) approaches were applied to calculate K_fs (Reynolds and Elrick, 1990). A constant value of the *-parameter, equal to 12 m^–1, was used for the OPD approach.

The geometric mean and the associated coefficient of variation were calculated for the K_fs results obtained in the field with both the SFH and PI experiments because they were found to be log-normally distributed (data not shown).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Laboratory Experiments
On average, the ECH K_fs estimate of the undisturbed soil cores was 1.82 times less than the value determined by the SFH technique and the two techniques produced values of CV differing by a factor of 1.04 (Table 2). Correlation between the log-transformed values of K_fs obtained with the two techniques was statistically significant (P = 0.05, coefficient of determination, r² = 0.65). However, the observed discrepancies are negligible from a practical point of view, given that many authors have suggested that an error of the estimate of K_fs by a factor of two or three can be considered acceptable for many practical purposes (Elrick and Reynolds, 1992a; Reynolds and Zebchuk, 1996; Elrick et al., 2002). A tendency of the SFH technique to produce higher values of K_fs as compared with the ECH technique was however recognized. We felt two possible reasons for the observed discrepancies. First, a short-term surface soil structure degradation has been recognized to determine a reduction of K_fs measurements conducted repeatedly on a given soil core (Bagarello et al., 2000). The ECH experiments were conducted after the SFH experiments that, likely, were effective in promoting some form of degradation of the upper layer of the core. Second, the initial soil water content was higher for the ECH experiments (mean = 0.191 m³ m^–3, CV = 40.1%) than for the SFH experiments (mean = 0.248 m³ m^–3, CV = 23.8%). Probably closure of macropores occurred as the soil water content increased and this determined a reduction of hydraulic conductivity.

The TPD approach produced positive values of K_fs and * for 21 PI experiments (success rate = 72%, = 6.29 x 10^–6 m s^–1, CV = 198.6%). For these experiments, the geometric mean value of * was equal to 9.5 m^–1 and this result supported the choice of using * = 12 m^–1 for the OPD calculations. This level of support was considered to be enough for this investigation because the sensitivity of * to measurement errors using the TPD approach is high and reasonably accurate estimates of K_fs can be obtained using * values that are largely erroneous (Mertens et al., 2002). The K_fs values obtained by the OPD approach were used in the method comparison to include data from all sites.

The two sets of SFH experiments produced values that differed by a factor of 1.93 and that were 1.14 (second set) to 2.20 (first set) times higher than the value obtained with the PI technique (Table 4). The CVs of the K_fs data obtained with the transient approach were similar, differing by a factor of 1.11, and they were 1.73 to 1.92 times lower than the CV value calculated for the steady-state results. The first and the second application of the SFH technique yielded higher K_fs results than the PI technique for 24 (80% of the total) and 14 (47% of the total) experiments, respectively. The maximum values of K_fs obtained with the first set of SFH experiments (K_fs = 4.05 x 10^–5 m s^–1) and the PI technique (K_fs = 3.58 x 10^–5 m s^–1) were similar and they were approximately two times higher than the maximum K_fs measured with the second application of the SFH technique (K_fs = 1.79 x 10^–5 m s^–1). In all cases, a statistically significant (P = 0.05) correlation was detected between the log-transformed K_fs data, with values of r² ranging from 0.51 (first SFH experiment vs. PI experiment) to 0.77 (first SFH experiment vs. second SFH experiment).

An attempt to interpret the K_fs results was made notwithstanding that this can be an imprecise enterprise due to the lack of independent K_fs datum or benchmark on which evaluations and judgments can be made (Reynolds et al., 2000).

The sampled soil volumes were wetted only once before the first SFH experiment and on several occasions before the second SFH experiment and this probably contributed to the observed discrepancies between the two sets of SFH data. Maintaining moist conditions for an extended period likely promoted some form of soil structure weakening that reduced macroporosity (Beven and German, 1982; Hillel, 1998) and increased biological activity (McKenzie et al., 2001). These factors probably led to a general reduction in the K_fs of the upper soil layer sampled by the SFH technique.

An implication of this interpretation is that the results of the first set of SFH experiments should be considered as a more meaningful comparison between the SFH and PI techniques. Structure modification induced by wetting processes between the first SFH experiment and the PI experiment was negligible since in practice the soil was only wetted by the water supplied with the SFH experiment. Natural soil structure modifications were also negligible because the PI experiment was conducted a relatively short time after the first SFH experiment (with a few exceptions, <25 d).

The method comparison showed that the SFH technique tended to produce slightly higher and less variable K_fs results than the PI technique. Probably, the different duration of the two types of experiment contributed to this discrepancy. During a ponded infiltration experiment, the ability of the largest pores to transport flow likely decreases as the duration of the experiment and the sampled soil volume increases. This depends on the fact that both the tortuosity of the flow pathways (Hillel, 1998) and the potential for the occurrence of infiltration processes into the soil matrix through the large pore walls (Beven and German, 1982) tend to increase. Soil swelling can be also promoted by a long-duration infiltration experiment (Bagarello et al., 1999). Although the clay type was not determined, some soil swelling is expected to occur at the field site given that small cracks (i.e., <0.01 m large) were observed under dry conditions in the undisturbed areas of the field. All these factors reduce the rate of water entry into the soil through the infiltration surface. Consequently, a long-duration experiment can yield a value of K_fs equal to or lower than a short-duration experiment. Soil properties controlling flow transport (e.g., size, shape, and connectivity of the pores) vary greatly in space (Warrick, 1998) and therefore the differences in K_fs obtained by the two approaches are expected to be site-dependent. A higher frequency of low K_fs is however expected and this can produce a higher variability of the individual measurements.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Measuring K_fs at a great number of locations over a large area with a realistic use of resources in terms of time and costs needs a short duration experiment, small volumes of water and easily transportable equipment.

A SFH technique for the rapid determination of K_fs has been proposed and verified here. The technique consists of applying quickly a small volume of water on the soil surface confined by a ring inserted a short depth into the soil and then measuring the time from the application of water to the instant at which the surface area is no longer covered by water. This time, together with a measurement of initial and field-saturated soil water content and an estimate of the *-parameter, is used to calculate K_fs by a simple solution based on the GA assumptions. This solution includes gravity. The duration of the experiment ranges from <5 min for permeable soils (i.e., K_fs 1 x 10^–4 m s^–1) to more than 3.5 h for soils with a relatively low permeability (i.e., K_fs 1 x 10^–8 m s^–1). This theoretical analysis suggested that the SFH technique could be potentially applied to a broad range of soils, working faster and easier in permeable and moderately permeable soils. Minor errors (i.e., ±10% of the true value) in the measurement of the initial water depth, the duration of the infiltration process or the soil water content do not affect appreciably the determination of K_fs. The SFH technique can also be used to measure K_fs of detached soil cores.

Laboratory tests were conducted to ascertain the accuracy to which this SFH technique could estimate K_fs, compared with the ECH technique. This last technique is one of the simplest techniques that use the initial period of the infiltration process to deduce K_fs. An ECH experiment was conducted a few days after an SFH experiment on nine undisturbed soil cores. The mean value of K_fs obtained by the ECH technique was 1.82 times less than the corresponding value determined by the SFH technique and the associated coefficients of variation differed by a factor of 1.04. The observed discrepancies were small from a practical point of view and they were attributed to some form of surface soil degradation and closure of macropores promoted by the SFH experiment. Forty-two identical soil columns were also prepared and each technique was applied to about one half of the soil columns. Very similar estimates of both mean (i.e., differing by a factor of 1.23) and CV (i.e., differing by a factor of 1.05) of K_fs were obtained. We feel these results represent a good agreement between the ECH and SFH techniques.

A field test was conducted in a loamy soil to compare the SFH technique to the classical PI technique. The values of K_fs measured at 30 sites by the SFH technique were 2.0 times higher and 1.92 times less variable than the corresponding values obtained by the PI technique, suggesting that the two techniques yielded a similar estimate of the mean value of K_fs. The discrepancies between the SFH and the PI results were attributed to a decrease in the ability of the largest pores to conduct flow as the duration of the experiments and the sampled soil volume increased.

In all cases, the SFH technique appeared very promising since it yielded estimates of differing by a maximum factor of two from those obtained by other techniques, both in the laboratory and in the field. In addition, the SFH technique appears to be simpler than the ECH and PI techniques used in this investigation for comparative purposes. In fact, the falling head technique is based on a simple and generally rapid experiment in the field (especially at the soil surface) and it requires standard and easily usable laboratory equipment, such as an oven and a balance. A large ring (0.20–0.30 m diam.) and a small volume of water (<1 L) could be used so that a larger representative elementary volume could be sampled. Vertical variations of K_fs could be assessed with a high resolution by carrying out infiltration tests at closely spaced depths, given that a small depth of soil is sampled. Especially in moderately permeable soils, many experiments could be conducted simultaneously by one person. The proposed technique appears promising for determining K_fs in a relatively short period of time without the need for extensive instrumentation or analytical methodology and therefore appears suitable for detailed sampling over large areas.

	ACKNOWLEDGMENTS

 
V. Bagarello and M. Iovino thank Giovanna Costa for her competent technical assistance in field data collection and Barbara Calaciura who conducted most of the laboratory experiments used in this study for her Degree Thesis. This study was supported by grants from the Italian Ministero dell'Istruzione, dell'Università e della Ricerca, Program PRIN 2000 "Impiego di modelli di simulazione nella gestione dell'irrigazione".

Received for publication February 13, 2003.

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TOP ABSTRACT INTRODUCTION A Review of Some... The Simplified Falling-Head... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

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