A field assessment of the Simplified Falling Head technique to measure the saturated soil hydraulic conductivity

Geoderma 187–188 (2012) 49–58

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A field assessment of the Simplified Falling Head technique to measure the saturated soil hydraulic conductivity V. Bagarello ⁎, F. D'Asaro, M. Iovino Dipartimento dei Sistemi Agro-Ambientali, Facoltà di Agraria, Università degli Studi, Viale delle Scienze, Palermo, Italy

a r t i c l e

i n f o

Article history: Received 10 October 2011 Received in revised form 15 March 2012 Accepted 14 April 2012 Available online 23 May 2012 Keywords: Field saturated soil hydraulic conductivity Measurement techniques Simplified Falling Head technique

a b s t r a c t The Simplified Falling Head (SFH) technique to measure field saturated soil hydraulic conductivity, Kfs, has received little testing or comparison with other techniques. Different experiments were carried out to i) determine the effect of ring size on the measured conductivity; ii) compare the SFH and Pressure Infiltrometer (PI) techniques in a clay loam soil; and iii) evaluate the approach used in the SFH methodology to estimate the α* parameter. Sampling a relatively large number of sites allowed to detect statistically significant relationships between the Kfs values obtained with rings differing in diameter (0.15 and 0.30 m, respectively). The ring size effect was substantial (factor of discrepancy between Kfs results of more than an order of magnitude) for low Kfs values (~2 mm h− 1) but it was practically negligible (factor ≤ 1.7) for high conductivities (Kfs ≥ 350 mm h− 1). Data supporting the hypothesis that the detected ring size effect was an effect of the different total area sampled with the two rings were obtained. A test carried out with a small ring contained enough information to approximately predict the Kfs value that would be obtained with a larger ring. The SFH and PI techniques yielded statistically similar means of Kfs but substantially different coefficients of variation, that was particularly high for the SFH technique. The duration of the infiltration run, appreciably shorter for the SFH than the PI technique with the Two‐Ponding Depth approach, probably influenced swelling phenomena of the field soil during the run and this circumstance determined the detected discrepancies. The two techniques should be considered complementary, being usable to determine Kfs at the beginning (SFH) and at a later stage (PI) of a ponding infiltration process. Using α* values directly measured by the tension infiltrometer or estimated on the basis of a general description of soil characteristics did not affect significantly the results of the SFH technique. Therefore, the approximate criterion to estimate α* was appropriate. In conclusion, this investigation gave support to the use of the SFH technique for a rapid and reasonably simple approximate determination of Kfs. Developments should consider a transient, three-dimensional infiltration process established by a ring inserted a short distance into the soil. © 2012 Elsevier B.V. All rights reserved.

1. Introduction 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 (Reynolds et al., 2000). Especially for structured soils, saturated hydraulic conductivity should 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). Reliable field data should be collected with a reasonably simple and rapid experiment. Bagarello et al. (2004) proposed the Simplified Falling Head (SFH) infiltrometric technique for rapid determination of field saturated soil hydraulic conductivity, Kfs, of initially unsaturated soil (i.e., the ⁎ Corresponding author. Tel.: + 39 0917028108; fax: + 39 091484035. E-mail address: [email protected] (V. Bagarello). 0016-7061/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.geoderma.2012.04.008

soil is not saturated at the beginning of the experiment) using small volumes of water and easily transportable equipment. This technique was applied to monitor temporal changes in Kfs at the surface of a sandy loam soil (Bagarello and Sgroi, 2007), to characterize a clay soil at the plot scale (Bagarello et al., 2010), and to establish a comparison between pasture and forest soils (Agnese et al., 2011). The SFH technique was also used by other Authors, including Azam (2005), Shivakoti (2005), Rex and Dubé (2006), Waugh et al. (2006), Azam et al. (2008), Rojas et al. (2008). However, the SFH technique has so far received little field testing or comparison with other techniques. Issues needing specific consideration include i) dependence of the estimated conductivity on ring size; ii) relative performances of the SFH and other Kfs measurement techniques in relatively fine textured soils; and iii) reliability of the approximate approach used to estimate the so‐called α* parameter, equal to the ratio between Kfs and the matric flux potential. The size of the individual soil sample is known to influence measurement of soil hydrodynamic parameters both in the laboratory

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V. Bagarello et al. / Geoderma 187–188 (2012) 49–58

and the field (Anderson and Bouma, 1973; Lai et al., 2010; Lauren et al., 1988). With the SFH technique, compaction or shattering phenomena during ring insertion (Reynolds, 1993), preferential flow at the interface between the inner ring wall and the soil (Chappell and Ternan, 1997), and blocking of non vertical macropores near the wall edges (Haws et al., 2004; Shouse et al., 1994; Wuest, 2005) cannot be excluded in principle, due to the relatively deep ring insertion into the soil. The possible occurrence of these phenomena implies that a large ring should be expected to yield more reliable Kfs data than a small ring. In a sandy loam soil, the comparison between a classical ring inserted into the soil and a casing realized with polyurethane foam suggested that ring insertion did not have an adverse impact on the quality of the Kfs measurements (Bagarello et al., 2009). However, additional investigations are necessary to better establish sample size effects on Kfs values obtained by the SFH technique, since only a few data have been specifically collected with reference to a one dimensional, transient, field infiltration process. Moreover, simple predictive methods of sample size effects on Kfs measurements are lacking. According to Reynolds et al. (2000), comparing techniques for measuring Kfs is an imprecise, perhaps even dubious, enterprise because there is no independent Kfs datum or benchmark upon which evaluations and judgments can be made. It is nonetheless important to make such comparisons because they provide one of the few sources of information that practitioners can draw upon to select Kfs methods that are appropriate for their circumstances. The single ring Pressure Infiltrometer (PI) (Reynolds and Elrick, 1990) is a good technique for a comparison with the SFH one for different reasons including the simplicity of the experiment in the field, the reliability of the Kfs results (Reynolds et al., 2000), and the similarity of the sampled soil volumes (Bagarello et al., 2004). The few available comparisons between the SFH and PI techniques were encouraging, generally suggesting a similarity of the Kfs values obtained with two techniques, but they were limited to relatively coarse textured soils (Bagarello and Sgroi, 2007; Bagarello et al., 2004, 2006). Therefore, there is the need to also compare these two techniques in finer soils. The reliability of the measurement of Kfs by the SFH technique depends on the α* parameter, that is estimated by a table considering only four categories of soils (Elrick and Reynolds, 1992). According to the theoretical analysis by Bagarello et al. (2004), an improper evaluation of α* by one category determines an acceptable error in the estimate of Kfs for many practical applications. However, extreme values of α*, also falling outside a much wider range (0.1 ≤ α* ≤ 1000 m − 1) than the one (1 ≤ α* ≤ 36 m − 1) suggested by Elrick and Reynolds (1992), can be found in the literature (Khaleel and Relyea, 2001; Russo et al., 1997; White and Sully, 1992). Therefore, additional investigations on the practical usability of the table by Elrick and Reynolds (1992) with the SFH technique are necessary. The tension infiltrometer (TI) method (Perroux and White, 1988; Reynolds and Elrick, 1991) appears particularly suited to experimentally determine the α* parameter because it can be used to establish quasi saturated conditions, that are close to the ones established for the measurement of Kfs, with a minimum field soil disturbance. Other ponding infiltration techniques, such as the PI one, seem to have a reduced interest in this case because the quality of the estimated α* parameter is expected to be questionable (Bagarello et al., 2000; Mertens et al., 2002; Reynolds and Elrick, 1990). The general objective of this investigation was to improve our knowledge on the reliability of a field measurement of saturated soil hydraulic conductivity by the Simplified Falling Head technique. The specific objectives were to: i) determine sample size effects on field saturated soil hydraulic conductivity measurements; ii) compare the SFH and PI techniques for a relatively fine textured soil; and iii) assess the usability of a literature estimate of the α* parameter.

2. Theory The SFH technique (Bagarello et al., 2004) consists of quickly pouring a known volume of water, V (L 3), on the soil confined by a ring inserted a fixed distance into the soil, d (L), and in measuring the time, ta (T), from the application of water to the instant at which the surface area, A (L 2), is no longer covered by water. The field saturated soil hydraulic conductivity, Kfs (LT − 1), is determined by the following equation, based on the analysis by Philip (1992) for falling head one dimensional cumulative infiltration: " !#
 1 D þ α ð1−ΔθÞD Δθ D  ln 1 þ
− K fs ¼ 1 1−Δθ ð1−ΔθÞt a Δθ Δθ D þ α

ð1Þ

where Δθ (L 3L − 3) is the difference between the field saturated (θfs) and the initial (θi) volumetric soil water content, D = V/A (L) is the depth of water corresponding to V, and α* (L − 1) is a soil texture/ structure parameter, that can be estimated according to Elrick and Reynolds (1992). Knowledge of Δθ and d allows 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 has to be used to assure one dimensional flow during the experiment. Since Eq. (1) includes gravity, the only time limitation will occur if the wetting front emerges from the bottom of the ring and three‐dimensional flow commences. 3. Materials and methods Three different experiments were carried out in this investigation. The first experiment was aimed to establish ring size effects on the measured conductivity. A comparison between the SFH and PI techniques for a relatively fine textured soil was carried out in the second experiment. The effect of the α* parameter estimation method (from the literature, measured by the TI technique) on the Kfs calculations was determined with the third experiment. 3.1. Ring size effects on field saturated hydraulic conductivity The SFH technique was applied at 24 sites randomly selected within the Imera Meridionale watershed, in Sicily (Fig. 1), with large differences in both soil texture and land use (Table 1). For a given site, having an area of approximately 25 m 2, ten undisturbed soil cores (0.05 m in height by 0.05 m in diameter) were collected at the 0 to 0.05 m and 0.05 to 0.10 m depths in five randomly selected points. Five disturbed soil samples (0–0.10 m depth) were also collected. The undisturbed soil cores were used to determine in the laboratory the dry soil bulk density, ρb (Mg m − 3), and the soil water content at the time of sampling, θi (m 3m − 3). The disturbed soil was used to determine the particle size distribution (PSD), using conventional methods following H2O2 pre-treatment to eliminate organic matter and clay deflocculation using sodium metaphosphate and mechanical agitation (Gee and Bauder, 1986). Fine size fractions were determined by the hydrometer method, whereas the coarse fractions were obtained by mechanical dry sieving. The experimentally determined PSD was used to determine the clay (cl), silt (si) and sand (sa) percentages according to the USDA standards (Gee and Bauder, 1986). The organic carbon, OC (%), content, measured by the Walkley–Black method, was converted to organic matter, OM (%), content using the factor of conversion of 1.72. Five random points were sampled to determine Kfs by the SFH technique using 0.15 m diam. rings (Kfs15). Other five random points were sampled with a 0.30 m diam. ring (Kfs30). In all cases, the depth of insertion of the ring was equal to d = 0.12 m. Ring insertion was conducted by gently using a rubber hammer and ensuring that the upper rim of the ring remained horizontal during insertion. The

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Imera Meridionale and DIFA sites Ring size effect experiment Castelvetrano SFH vs. PI comparison Dirillo α* estimation experiment Fig. 1. Locations of the sampling areas and sites in Sicily.

volume of voids within the soil volume confined by the ring was not known before performing the infiltration test in the field because sampling soil and carrying out the necessary laboratory measurements was not practical due to the distance between the watershed and the laboratory. For each site, however, the soil bulk

density and the soil water content corresponding to selected pressure head values (h = −0.1, −1, and −150 m) were also determined several weeks to months before the SFH campaign. This information was used to determine the V volume for a given site. In particular, an estimate of θfs was obtained using the measured ρb and

Table 1 General characteristics of the sampled sites. Project

Imera Meridionale

DIFA

Site code

22 32 59 61 64 66 67 69 72 82 83 85 86 93 97 101 103 104 108 110 111 112 115 153 AGR1 AGR2 CACC COR1 COR2 COR3 COR4 COR5 SPA1 SPA2

UTM coordinates 33S N (m)

E (m)

4177550 4174925 4165925 4165530 4165425 4165600 4165800 4162725 4162715 4156730 4156640 4156510 4156425 4150320 4150615 4147620 4147436 4147400 4147575 4147635 4147520 4147380 4144610 4138690 4219144 4219144 4193034 4186142 4186076 4187747 4187685 4187509 4166290 4166290

407210 411090 412475 418070 427475 434020 436490 415610 425080 421900 426050 433030 436700 418350 430150 406603 412698 414590 427175 433700 436800 439700 406830 439490 355578 355578 380862 350099 350054 349619 349604 347282 390947 390947

Soil use

Clay (%)

Silt (%)

Sand (%)

Soil textural class

Organic matter content (%)

Annual crops Annual crops Annual crops Bare soil Pasture Pasture Pasture Almond grove Annual crops Pasture Annual crops Almond grove Pasture Eucalyptus Annual crops Olive grove Citrus orchard Citrus orchard Annual crops Olive grove Pasture Eucalyptus Annual crops Pasture Citrus orchard Citrus orchard Annual crops Vineyard Annual crops Vineyard Orchard Olive grove Orchard Orchard

43.0 22.2 47.8 41.4 43.0 16.4 39.0 61.8 10.7 9.1 57.9 41.9 42.2 21.9 31.5 27.1 21.5 29.6 62.8 59.5 30.3 12.9 60.7 9.1 15.9 19.2 34.6 49.6 57.1 49.0 52.6 17.3 11.6 22.0

32.7 27.2 31.8 52.1 52.0 17.2 19.9 32.9 79.3 13.4 30.9 51.0 31.2 29.7 46.6 48.2 17.8 31.7 31.2 28.9 19.1 4.9 34.6 9.6 27.2 32.5 45.8 33.2 30.7 35.3 35.8 30.5 22.2 19.7

24.3 50.6 20.4 6.5 5.0 66.4 41.1 5.3 10.0 77.5 11.2 7.1 26.6 48.4 21.9 24.7 60.6 38.7 6.1 11.6 50.6 82.2 4.7 81.3 56.9 48.3 19.6 17.3 12.2 15.7 11.6 52.3 66.2 58.2

Clay Sandy clay loam Clay Silty clay Silty clay Sandy loam Clay loam Clay Silt loam Sandy loam Clay Silty clay Clay Loam Clay loam Clay loam Sandy clay loam Clay loam Clay Clay Sandy clay loam Sandy loam Clay Loamy sand Sandy loam Loam Silty clay loam Clay Clay Clay Clay Sandy loam Sandy loam Sandy clay loam

2.0 2.0 2.0 3.4 2.9 2.8 2.4 2.3 2.5 0.7 1.8 2.1 2.8 3.0 1.8 2.5 2.1 2.8 1.4 1.3 1.4 2.2 2.0 1.1 4.5 3.5 1.5 2.8 1.4 2.0 2.1 1.9 0.5 0.5

The clay, silt, sand, and organic matter percentages are the means of five (Imera Meridionale project) or four (DIFA project) replicated measurements. AGR2 and SPA2 sites were close to the AGR1 and SPA1 sites, respectively, but sampling was carried out in a different period of the year (summer for AGR1 and SPA1 sites, late fall for AGR2 and SPA2 sites).

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considering a soil particle density of 2.65 Mg m − 3 (Bagarello et al., 2004; Mubarak et al., 2009). As a precaution, the initial soil water content was set equal to the one corresponding to the so-called field capacity (h = − 1 m). A similar precautionary approach was applied by Bonnell and Williams (1986) to maintain one dimensional flow during their single ring infiltration experiments. The ρb and θi values obtained at the time of the SFH experiment were used to control that flow was really one dimensional during each SFH run and also to calculate Kfs by Eq. (1). All measurements were carried out from April to August 2007. Ten additional sites (Fig. 1) were sampled in the last six months of 2010 for the DIFA project of the Sicilian Region. The applied procedure was similar to the one used in the Imera Meridionale watershed, although four sampling points were considered at a given site (Table 1) instead of five. In addition, undisturbed soil cores were collected two or three days before performing the SFH infiltration test, and the values of ρb and θi measured on these cores were used to determine θfs and V. This investigation was based on the premise that a point or a small area in the field is better characterized by averaging a few, closely spaced replicated measurements of Kfs rather than by a single Kfs measurement. The practice to characterize soil at the practically point scale by replicating infiltration measurements at a few (i.e., two or three) locations was applied by other Authors, recently including, for example, Gonzalez-Sosa et al. (2010) and Price et al. (2010). For a given site, a data set was summarized by calculating the mean, M, and the associated coefficient of variation, CV. In particular, the arithmetic mean and the associated CV were calculated for cl, si, sa, OM, ρb and θi. Two means were obtained for each of these last two variables, considering separately the upper (0–0.05 m) and the lower (0.05–0.10 m) soil layer. These two means were further averaged to apply Eq. (1). For both Kfs15 and Kfs30, the statistical frequency distribution of the data was assumed to be log-normal, as is common for Kfs (e.g. Mohanty et al., 1994; Warrick, 1998). Therefore, geometric means and associated CVs were calculated using the appropriate “log-normal equations” (Lee et al., 1985). The factor of discrepancy between the measured Kfs15 and Kfs30 values was calculated as a = abs[log10(Kfs15/Kfs30)] to obtain the same magnitude when the factor of difference is the same (for example, a = 0.301 for Kfs15/Kfs30 equal to both 0.5 and 2.0) (Beckwith et al., 2003).

3.2. Comparing the SFH and PI techniques This investigation was carried out in the period February to March 2008 at the CLV site, near Castelvetrano, in Sicily (Fig. 1), where a 400 m 2 flat area of an olive grove, with trees spaced 8 m × 5 m apart, was selected. The soil was a Typic Haploxeralf having a clay loam texture in the upper layer, 0.15 m thick (cl = 29.1%; si = 32.0%; sa = 38.9%). A single ring Pressure Infiltrometer (PI) test was conducted at each of 20 randomly chosen locations within the experimental area, using a device similar to the one designed by Ciollaro and Lamaddalena (1998). A ring with an inner diameter of 0.15 m was inserted to a depth d = 0.12 m, after removing the first few centimeters of soil. A constant depth of ponding, H1 = 0.053 m, was established on the soil surface and flow rate was monitored to detect steady state conditions. A constant depth of ponding, H2 = 0.11 m, was then established and flow rate was monitored until another quasi steady state condition was reached. Apparent steady state flow rates (Qs1 and Qs2) corresponding to the two applied H levels (H1 and H2) were estimated from the flow rate versus time plot. The total duration of the run varied between 178 and 211 min, depending on the test, and the time interval between readings was of 0.5 to 2.0 min. Two undisturbed soil cores (0.05 m diam. by 0.05 m high) were collected near the ring at a depth of 0 to 0.05 m and 0.05 to

0.10 m, respectively, before the PI test. These cores were used to determine an averaged ρb and θi value over the two sampled depths. The SFH technique was also applied in 20 randomly chosen locations during the PI measurement period, to obtain a set of Kfs data usable for comparative purposes. Also in this case, a ring with an inner diameter of 0.15 m was inserted to a depth, d = 0.12 m, after removing the first few centimeters of soil. To obtain the V values for the SFH runs, two undisturbed soil cores (0.05 m diam. by 0.05 m high) were collected at a depth of 0 to 0.05 m and 0.05 to 0.10 m, respectively, two days before the SFH experiment. Taking into account that small uncertainties in the estimated Δθ do not affect appreciably the estimate of Kfs (Bagarello et al., 2004) and a low to medium spatial variability is expected for both θi and ρb at the field scale (Warrick, 1998), a single point was sampled on a given day and the θi and ρb results were assumed to be usable for the SFH tests carried out two days later. Obviously, the locations for these infiltration tests were reasonably close (i.e., at the most, 2 m) to the point where the undisturbed soil cores were collected. Therefore, the SFH technique was applied in a particularly simplified way in this investigation. The Two-Ponding-Depth (TPD) approach by Reynolds and Elrick (1990) was applied for each PI run to estimate Kfs and α* at each measurement location. The One-Ponding-Depth (OPD) calculation approach (Reynolds and Elrick, 1990) was also applied by considering the first ponded level (H1). Eq. (1) was used to calculate Kfs for each SFH test. According to Elrick and Reynolds (1992), a value of α* = 12 m − 1 was used for these last two calculations. Geometric means and associated CVs were calculated to summarize the Kfs data sets. Rings with an inner diameter of 0.15 m were used in this experiment to obtain easily comparable data with other investigations (Bagarello and Sgroi, 2007; Bagarello et al., 2004). Moreover, a comparison based on 0.15 m rings was thought to have more practical interest than a comparison established with larger ring diameters because relatively small diameter surfaces (b0.10–0.15 m) are frequently sampled with the infiltrometric techniques, and larger diameters are seldom used mainly because they complicate appreciably the experiment in the field. 3.3. Effect of the α* parameter determination method This investigation was carried out in the period September 2008 to February 2009 in the valley portion of the Dirillo watershed, in Sicily (Fig. 1), having an area of approximately 3000 ha. A total of 27 sites, each of approximately 8 m 2, were established in soils differing by texture. In particular, soil texture was clay loam (two sites), loam (nine), loamy sand (two), sandy (one), sandy loam (seven), silt loam (two), silty clay (two), and silty clay loam (two). Two infiltration runs with the tension infiltrometer (TI) and two SFH experiments were carried out at each site in different sampling locations established at a maximum distance of approximately 1 m (Fig. 2). Two replicates were considered at a given point for practical reasons, related to the relatively long duration of the TI runs in the field. The TI used in this investigation had a 0.22 m diam. base plate unit, with a separated water supply unit to prevent compaction of the soil surface during the experiment. At a given sampling location, the soil surface was carefully leveled and smoothed before each experiment and attempts were made to prevent infiltration surface smearing. A thin (≤10 mm thick) layer of contact material (Bagarello et al., 2001; Reynolds, 2006; Reynolds and Zebchuk, 1996) was placed over the surface to fill small depressions and to improve the contact between the soil and the disk of the infiltrometer. A bubble level was used to ensure that the disk and the reservoir base were always at the same height (zero relative distance), so that the head between the bubbling outlet at the bottom of the

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4. Results and discussion 4.1. Ring size effects on field saturated hydraulic conductivity

water supply tubes and the disk membrane was constant. A multipotential experiment was carried out applying an ascending sequence of pressure heads, h0 (L), at the soil surface (− 120, −60, −30 and −10 mm), to exclude the effects of hysteresis on the measured soil hydraulic conductivity (Bagarello et al., 2005, 2007; Reynolds and Elrick, 1991). The duration of the experiments was >40 min for h0 = −120 mm, >30 min for h0 = −60 mm, >20 min for h0 = −30 mm, and >10 min for h0 = −10 mm. Visual readings of the water level in the supply tube of the infiltrometer were taken at 0.5 to 2 min intervals. In all cases, apparent steady state conditions were reached and an estimate of the apparent steady state infiltration rate was deduced from the slope of the linear portion of the cumulative infiltration vs. time plot (Bagarello et al., 1999). Immediately after application of the last pressure head, the visible wetted area at the surface, A (L 2), was determined by assuming the form of an ellipse and measuring the two principal axes. Before each experiment, an undisturbed soil sample was collected in close vicinity to the infiltration surface in 0.05-m-diam. by 0.05-m-high cylinders to determine θi. Soil hydraulic conductivity at the imposed pressure heads (K− 120, K− 60, K− 30, K− 10) and the parameter of the Gardner's (1958) exponential relationship between K and h were calculated by the piecewise exponential method (Reynolds and Elrick, 1991), based on the logarithmic transformation of Wooding's (1968) equation. The procedure used to perform the SFH run was similar to the one applied at the Imera Meridionale watershed because selected water retention points were determined at each site of the Dirillo watershed in a previous investigation (Antinoro et al., 2008). Also in this case, however, both ρb and θi at the time of the SFH test were determined to control that flow was one dimensional during the run and also to calculate Kfs by Eq. (1). Two Kfs values were calculated at a given location. An estimate of Kfs was obtained by choosing α* from the literature, i.e. using the table by Elrick and Reynolds (1992), as suggested by Bagarello et al. (2004). In particular, α* = 4 m − 1 was used when the soil at the sampling point had a sand content, sa b 20%. An α* value equal to 12 m − 1 was used for 20 ≤ sa ≤ 70%, and α* = 36 m − 1 was used in soils with sa > 70%. These estimates of Kfs were denoted by the symbol KfsL. Another Kfs value was obtained by using the estimate of α* corresponding to the two highest pressure heads (−30 and −10 mm, i.e. close to saturation) established with the TI. These estimates of Kfs were denoted by the symbol KfsTI. For a given site, the duplicated K and Kfs data were averaged to obtain a site-representative result. Only the sites giving K− 120 b K− 60 b K− 30 K− 10 b KfsL and KfsTI were considered for the analysis.

1 0.8

Frequency

Fig. 2. View of the field experiment at a site of the Dirillo watershed.

Independently of the sampling depth, the ρb data obtained for the Imera Meridionale and DIFA projects were less variable than the θi ones (Fig. 3), as expected. In particular, the 68 coefficients of variation of ρb did not exceed 0.14 with a single exception (CV = 0.21), confirming the suggestion by Warrick (1998) that soil bulk density is expected to show a low variation (i.e., CV b 0.15). A low to medium variation, i.e. CV values not exceeding 0.5 (Warrick, 1998), was detected for θi with two exceptions yielding however CV results very close to 0.5 (i.e. 0.502 and 0.55). The ring size effect on the measured conductivities (Table 2) was determined considering that data had a hierarchical structure given that a few independent measurements were carried out at a given site for a given ring size. To be clearer, the hierarchy was due to the fact that, for the two ring sizes, 34 sites were randomly selected and four or five runs were randomly carried out at a given site with each ring size. Therefore, Systat 11 (Systat Software, Inc., Chicago, IL, www.systat.com) was used to apply the Hierarchical Linear Mixed Model with ring size, clay content, sand content, organic matter content, and soil use (a categorical variable) as fixed effects, and site and run within site (replicate measurement) as random effects. The estimation method used was the Restricted Maximum Likelihood method. The results of this analysis showed that the ring size had a significant effect on the measured conductivity (Table 3). The random variable site explained the 58% of total variance of Kfs whereas the random variable run within site explained only the 7% of this variance. Therefore, the information obtained with reference to a relatively large number of sites with varying soil and land use was that the ring size used for the measurements affected the conductivity results. The high variance detected for the site factor denoted the importance that has to be assigned to a spatially representative sampling. To more clearly assess the ring size effect on the measured hydraulic conductivity, an analysis of the coefficients of variation and a linear regression analysis between Kfs and other soil properties were carried out. With a single exception yielding a low CV (=0.053), the CVs of Kfs denoted a medium (in 19 cases) or, more frequently (i.e., in 48 cases), a high variation of the individual measurements at a site (Fig. 3), as expected (Warrick, 1998). The maximum CV of Kfs was equal to 5.6 for the 0.30 m diam. rings and to 47.1 for the 0.15 m diam. ones. Nine CVs obtained with the small ring were higher than the maximum CV for the large ring. In general, both Kfs15 and Kfs30 were better correlated to independent variables indicative of

θi0-5 θi5-10 ρb0-5 ρb5-10 Kfs15 Kfs30

0.6 0.4 0.2 0 0.01

0.1

1

10

100

Coefficient of variation Fig. 3. Cumulative empirical frequency distribution of the coefficients of variation obtained at each site for the three sampled soil properties (sample size, N = 34 for the antecedent soil water content, θi, at the 0–0.05 m (0–5 in the figure) and 0.05– 0.10 m (5–10) depths, the associated dry soil bulk density, ρb, and the surface soil field saturated hydraulic conductivity measured with the 0.15 m diam., Kfs15, and 0.30 m diam., Kfs30, rings).

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Table 2 Mean (M) and coefficient of variation (CV, dimensionless) of the field saturated soil hydraulic conductivity, Kfs (mm h− 1), values at the sampled sites. Project

Imera Meridionale

DIFA

Site code

0.15-m-diam. ring

0.30-m-diam. ring

M

CV

M

CV

22 32 59 61 64 66 67 69 72 82 83 85 86 93 97 101 103 104 108 110 111 112 115 153 AGR1 AGR2 CACC COR1 COR2 COR3 COR4 COR5 SPA1 SPA2

40.5 28.4 413.7 33.4 175.8 11.8 1.7 4.8 4.8 98.6 17.6 30.3 806.6 451.5 16.5 970.5 33.0 377.8 11.1 42.3 4.9 161.3 1043.4 202.1 1195.5 299.2 254.8 838.1 414.2 7424.5 4288.2 282.2 131.0 156.1

19.31 33.91 2.85 32.33 4.20 2.16 0.38 2.67 5.56 0.31 10.71 47.11 3.09 0.25 38.99 0.69 2.46 43.66 7.38 6.27 0.05 0.48 0.89 0.47 0.27 0.91 0.51 0.33 1.71 0.63 0.74 0.65 0.40 0.63

491.3 51.2 535.2 193.3 626.7 44.7 15.6 42.3 28.7 96.4 242.8 46.8 3393.0 207.7 99.7 955.8 265.4 1349.6 158.3 159.1 27.5 135.3 862.5 166.3 1977.6 1021.4 583.9 4524.7 2808.5 4087.6 1822.2 309.8 83.9 57.5

5.58 0.89 0.79 1.56 0.56 0.41 3.05 3.01 1.61 0.41 1.19 1.65 1.18 0.60 4.51 0.34 1.67 0.45 3.92 1.97 1.62 0.47 1.93 0.50 0.20 0.27 0.41 0.22 0.87 0.66 0.19 1.54 0.53 0.52

soil structure, i.e., ρb and OM content, than to the textural ones, i.e. cl, si and sa content (Table 4). This result was plausible, being known that soil particle arrangement has a large influence on saturated hydraulic conductivity (e.g., Bouma and Dekker, 1981). The Kfs15 values decreased as ρb increased, but they did not vary with OM. On the other hand, Kfs30 increased with OM and decreased with ρb. The OM content should be expected to be positively correlated with saturated hydraulic conductivity because organic matter can stimulate soil aggregation, which lowers bulk density, increases porosity and hence elevates saturated conductivity (Agnese et al., 2011; Rawls et al., 2005). A negative correlation between ρb and OM has been found by several Authors (e.g., Ruehlmann and Körschens, 2009; Zacharia and Wessolek, 2007) and it was also detected in this investigation (R 2 = 0.129, R > 0). Therefore, both the CV comparison and the linear regression analysis suggested an effect of the ring diameter on the reliability of the Kfs data. In particular, the large diameter ring yielded more representative results than the small

Table 3 Summary of the results of the Hierarchical Linear Mixed Model. Effect

Factor

Variance

Random

Site Replicate (site) Error Ring size Soil use Sand Clay Organic matter

0.4946 0.0598 0.2899

Fixed

P value

b 10− 6 0.1610 0.6307 0.3396 0.1892

one since data were less variable and better correlated with other soil properties by physically convincing relationships. A higher CV of Kfs was obtained with the 0.15 m diam. ring than the 0.30 m diam. one in most cases, i.e. in the 71% of the sites. For these sites, the following equation, developed according to Warrick (1998), was used to estimate the number of runs with the smaller ring, N15, yielding the same tolerance of the larger ring experiment: N15 ¼

CV 215 N30 CV 230

ð2Þ

where CV15 and CV30 are the coefficients of variation of ln(Kfs15) and ln(Kfs30), respectively, and N30 is the number of replicated measurements with the 0.30 m diam. ring (N30 = 4 or 5, depending on the site). The log transformation was performed because Kfs was assumed to be log-normally distributed and the analysis was developed under the hypothesis of a normal population (Warrick, 1998). The N15/N30 ratio varied from 1.5 to 60.5, with a mean and a median of 10.5 and 5.8, respectively. Therefore, for a given tolerance, the practical simplification of using a relatively small ring in the field should generally expected to be counterbalanced by the need to perform an appreciably higher number of measurements. The dependence of the measured soil hydrodynamic properties on the sampled soil volume or surface area has been documented and physically explained in the literature (e.g., Anderson and Bouma, 1973; Bagarello and Provenzano, 1996; Haws et al., 2004; Lauren et al., 1988; Mallants et al., 1997; Shouse et al., 1994; Wuest, 2005; Youngs, 1987; Zobeck et al., 1985), and it was also confirmed for the SFH technique in this investigation. To our knowledge, however, little is known on the practical usability of a Kfs measurement carried out on a relatively small soil sample. In other words, the question is to establish if this measurement can be used to estimate the Kfs value that would be obtained with a more representative (i.e., larger) soil sample. Therefore, a linear regression analysis between Kfs30 and Kfs15 was carried out. According to a one tailed t test (P = 0.05), the linear regression of ln(Kfs30) (arithmetic mean of the five or four individual log-transformed measurements) against ln(Kfs15) yielded a statistically significant (i.e. >0) coefficient of correlation, R, for both data sets, with R 2 values equal to 0.705 for the Imera Meridionale data set and 0.553 for the DIFA one. Moreover, a coincidence test, applied to check the hypothesis that the two regression lines were similar at P = 0.05, suggested that fitting the two sets of data with separate regression lines was not better than fitting all the data with a single line. Therefore, the following relationship between the two variables was developed (Fig. 4):     ln K f s30 ¼ 2:5309 þ 0:6566 ln K f s15

ð3Þ

having R 2 = 0.719 (R > 0) and 95% confidence intervals for the intercept and the slope equal to 1.775–3.287 and 0.509–0.804, respectively. On average, the a index (=abs[log10(Kfs15/Kfs30)]) was equal to 4.4, but replacing the measured Kfs15 with the estimated Kfs30 by Eq. (3) determined a decrease of this index to 2.2. Therefore, Eq. (3) did not coincide with the identity line and it suggested that Kfs30 > Kfs15 should be expected for low Kfs values whereas more similar results occurs for high Kfs values. In particular, according to the fitted regression line the discrepancy between Kfs30 and Kfs15 was substantial (i.e., by a factor of 10.4) for the lowest measured Kfs15 value (~2 mm h − 1) but it was practically negligible (i.e., by a maximum factor of 1.7), according to several Authors (Elrick and Reynolds, 1992; Elrick et al., 2002), for the highest Kfs15 values (≥350 mm h − 1). Taking into account that an uncertainty in the estimate of Kfs by a factor of two or three is practically negligible (Elrick and Reynolds, 1992), Eq. (3) should be used, within the sampled range of conductivities, at least when the measured Kfs15 is less than 65 mm h − 1. The

V. Bagarello et al. / Geoderma 187–188 (2012) 49–58 Table 4 Intercept, b0, slope, b1, and coefficient of determination, R2, of the linear regression line between selected soil properties and the field saturated hydraulic conductivity measured with the 0.15 m diam. (Kfs15, in mm h− 1) and the 0.30 m diam. (Kfs30, in mm h− 1) rings (sample size, N = 34). Independent variable

Dependent variable ln(Kfs15) b0

cl si sa OM ρb

13.97

ln(Kfs30) b1

R2

b0

b1

R2

4.66

0.028

− 6.97

0.0013 ns 0.0009 ns 6.0 × 10− 5 ns 0.0246 ns 0.3229 s

4.31 13.13

0.061 − 5.65

0.0927 s 0.0101 ns 0.0729 ns 0.1118 s 0.3539 s

s: coefficient of correlation, R, significantly greater than zero according to a one tailed t test (P = 0.05); ns: coefficient of correlation, R, not significantly greater than zero.

developed equation should have a wide applicability, since it was obtained with reference to different soil textural classes and land uses (Table 1). Therefore, testing this equation in other environments is desirable, also considering that all sites were located in a particular Mediterranean region. Probably, the detected ring size effect can be explained by considering that, in soils with a relatively low conductivity, macropores or other small zones with a locally high conductivity are rare. Therefore Kfs30 > Kfs15 is the expected result because the wider surface sampled by the large ring implies a higher probability to intercept these zones. In soils with a relatively high conductivity, macropores or other high conductivity zones are more evenly distributed and even a small ring may yield a representative result, i.e. similar to the one obtained by a larger ring. A test of this hypothesis was carried out with reference to the Imera Meridionale database, having the highest number of replicated measurements for a given sampling point. In particular, the ln(Kfs30) vs. ln(Kfs15) relationship was determined by considering the mean of five replicated measurements of Kfs30 and i) the mean of five replicated Kfs15 data; ii) the mean of only three replicated Kfs15 values (10 possible combinations of individual measurements, i.e. ten Kfs30 vs. Kfs15 relationships); iii) the mean of two replicated Kfs15 data (ten Kfs30 vs. Kfs15 relationships); iv) and a single Kfs15 value (five Kfs30 vs. Kfs15 relationships). In other words, a Kfs value determined by sampling a relatively large surface area (Kfs30) was compared with the corresponding value obtained by sampling a lower and progressively decreasing area in the passage from point i) to point iv). A correlation coefficient significantly greater than zero (P = 0.05) was obtained for each developed relationship between ln(Kfs30) and ln(Kfs15), but an increasing number of replications for Kfs15 yielded higher values for both the slope (i.e., closer to 1) and the coefficient of determination, and lower values (i.e. closer to 0) for the intercept (Table 5). These results supported the hypothesis of a sampled area effect because sampling more similar surface

10

ln(Kfs30)

8 6 4 y = 0.6566x + 2.5309 R² = 0.7188

2 0 0

2

4

6

8

10

ln(Kfs15) Fig. 4. Relationship between the field saturated hydraulic conductivity measured with the large (Kfs30 in mm h− 1) and small (Kfs15 in mm h− 1) diameter rings at N = 34 Sicilian sites.

55

areas with the two rings improved the correlation and reduced the differences between the two datasets. According to this analysis, the scale effect should be practically negligible (intercept ≈ 0, slope ≈ 1) if the same total area is sampled with the two rings. Eq. (3), that is both mathematically and logically usable for Kfs15 > 0, allows to make a prediction of the Kfs30 value that would be obtained with a fixed number of replicated measurements if a smaller ring is used to perform the same number of runs. Using a General Linear Model with a stepwise selection of variables allowed to recognize that the estimate of Kfs30 can be improved if additional data (clay and organic matter content) are available. In particular, the following relationship was deduced:     ln K f s30 ¼ 0:793 þ 0:450 ln K f s15 þ 0:011cl h   þ 0:076 OM  ln K f s15 

ð4Þ

having an R2 of 0.919. For a given Kfs15 value, Kfs30 increased with both cl and OM within the sampled ranges of the two variables (9–63% for cl, 0.5–4.5% for OM). An implication of this result is that more noticeable scale effects should be expected in soils where primary particles tend to combine each other, whereas these effects are expected to be reduced in structureless soils. According to this investigation, the large ring should be used with the SFH technique instead of the small one, especially when the expected Kfs is relatively low. However, the developed equations established that the measurements carried out with the small ring contained enough information to make an approximate prediction of the Kfs values that would be obtained at the same site with the large ring. 4.2. Comparing the SFH and PI techniques The TPD approach yielded positive Kfs and α* results for 12 runs (success rate percentage = 60%) (Table 6), confirming that the two level analysis of ponding infiltration data may be problematic (i.e., small percentages of success rate) in fine textured soils, as already suggested for the Guelph permeameter technique (Elrick et al., 1990). The SFH technique yielded higher and much more variable Kfs results as compared with the PI technique, but the differences between the two techniques were not statistically significant according to a two tailed t test (P = 0.05), independently of the applied analysis procedure (TPD, OPD) of the PI data. Moreover, the transient and steady state techniques differed, in terms of mean Kfs value, by a maximum factor of three, that can be considered small from a practical point of view (Elrick and Reynolds, 1992; Elrick et al., 2002). Therefore, this investigation was in line with other investigations carried out in other soils (Bagarello and Sgroi, 2007; Bagarello et al., 2004). If the objective of the experiment is to obtain an estimate of the mean Kfs for an area of interest, the SFH technique is a practical alternative to the PI one also in relatively fine textured soils, given that the transient technique takes less time (mean duration of a SFH run = 65 min) and equipment as compared with the steady state one (mean duration of a PI run = 200 min; 111 min for the first ponding depth). Both techniques suggested a high variability of Kfs for the CLV site, but a much larger variability was obtained with the transient technique (CV = 17.2) than the steady state one (2.0 ≤ CV ≤ 3.5). A relative variability of several hundreds or also thousands percent for saturated soil hydraulic conductivity has been found in other investigations, including Anderson and Cassel (1986) (CV = 33.0) or Mallants et al. (1997) (CV = 9.0), but a very large variability suggests an uncertain representativeness of the calculated mean value. In any case, the large difference in the CV results of the two techniques needs an explanation.

V. Bagarello et al. / Geoderma 187–188 (2012) 49–58

Table 5 Intercept, b0, slope, b1, and coefficient of determination, R2, for the NR linear regression lines between the arithmetic mean of the five ln-transformed field saturated hydraulic conductivity values measured with the 0.30 m diam. ring and the corresponding value obtained with a varying number of data collected with the 0.15 m diam. ring, Kfs15. Replicated Kfs15 data

NR

b0

b1

R2

5 3 2 1

1 10 10 5

2.6903 2.6992–3.1385 2.9347–3.5427 3.4436–3.9923

0.6167 0.5079–0.6091 0.4253–0.5412 0.2993–0.4255

0.71 0.55–0.68 0.47–0.66 0.28–0.57

1 0.8

Frequency

56

0.6 SFH

0.4

TPD

0.2

OPD

0 0.1

For the PI method, the correlation between ln(Kfs) and either ρb or θi was not statistically significant, independently of the applied analysis procedure (i.e., TPD, OPD; ρb: 0.0038 ≤ R 2 ≤ 0.0043; θi: 9.0 × 10 − 5 ≤ R 2 ≤ 0.089; R = 0 according to a one tailed t test at P = 0.05). For the SFH technique, a weak but statistically significant correlation of ln(Kfs) with both ρb (R 2 = 0.162, R > 0) and θi (R 2 = 0.210, R > 0) was detected. In particular, Kfs was found to decrease as ρb and θi increased. The relatively short duration of the SFH run suggested that this test yielded a Kfs result which was representative of the soil conditions at the beginning, or the near beginning, of the ponding infiltration process. A relatively high θi value may be indicative of a reduced macroporosity due to swelling, an increased bulk density and a reduced saturated hydraulic conductivity. A relatively low value of θi may be indicative of more macroporosity, a lower bulk density and a higher Kfs. For the sampled site, this interpretation was supported by the existence of a statistically significant, positive relationship between θi and ρb (N = 26, i.e. SFH + PI data; R 2 = 0.606, R > 0). The PI run was relatively long. Therefore, it seems reasonable to suppose that the run promoted short term swelling phenomena reducing differences in macroporosity among sampling points. This circumstance, more than the amount of error in the measurements, precludes detection of a significant relationship between Kfs and either ρb or θi and also determines a decrease in both the mean and the relative variability of the measured conductivities. For this experiment the Kfs decrease was not large enough to determine statistically significant differences between the two Kfs measurement methods. Fig. 5 supports the suggested interpretation, showing that the two methods differed particularly in terms of maximum Kfs values, with the transient technique yielding an appreciable percentage of Kfs results higher than the maximum Kfs obtained with the PI method. According to the proposed interpretation, Kfs showed a noticeable spatial variability and it was relatively high in the early stage of a ponding infiltration process (SFH technique). When the infiltration process continued (PI method), phenomena such as soil swelling determined a closure of preferential pathways and this reduced both the mean Kfs value and the associated variability. A methodological implication of this interpretation is that the two methods can be considered complementary, being usable to determine Kfs at the beginning (SFH) and at a later stage (PI) of a ponding infiltration process in an initially unsaturated, relatively fine textured, soil.

Table 6 Summary statistics of the field saturated soil hydraulic conductivity, Kfs (mm h− 1), values obtained at the CLV site with the Simplified Falling Head (SFH) technique, and the single ring Pressure Infiltrometer method with both the Two-Ponding-Depth (TPD) and One-Ponding-Depth (OPD) approaches. Statistic

SFH

TPD

OPD

Sample size Minimum Maximum Mean Coefficient of variation

20 1.8 1124.3 38.5ab 17.23

12 0.6 110.0 12.9 ac 3.47

20 1.0 85.7 19.6bc 1.99

Values in a row followed by the same lower case letter are not significantly different according to a two tailed t test at the P = 0.05 probability level.

1

10

100

1000

10000

Kfs(mm h-1) Fig. 5. Cumulative empirical frequency distribution of the field saturated hydraulic conductivity, Kfs, values obtained with the transient SFH technique (sample size, N = 20) and the steady state single ring Pressure Infiltrometer method with both the Two‐ Ponding Depth (TPD, N = 12) and the One‐Ponding Depth (OPD, N = 20) calculation procedures.

According to Yair and Lavee (1985), the often brief duration of rain showers which originate from convective cells cause runoff to also be of short duration. Therefore, a measurement of Kfs at the beginning of a ponding infiltration process in an initially unsaturated soil may be important to predict the hydrological slope response when the soil is impacted by a rain shower with an initially very high intensity.

4.3. Effect of the α* parameter determination method Monotonically increasing K values from the lowest pressure head (−120 mm) to saturation conditions (KfsL and KfsTI) were obtained at 21 sites. Therefore, six sites were excluded from the analysis, mainly because either KfsL or KfsTI, or both, were lower than K− 10. Possible factors determining this result include presence of nearly horizontal macropores that did not contribute to the flow process established with the SFH run, soil compaction due to the ring insertion into the soil, or small scale spatial variability of soil hydraulic properties. The geometric mean value of the α* parameter obtained with the TI was equal to 16.3 m − 1 (Table 7), which is close to the value of first approximation suggested for most field soils (Elrick and Reynolds, 1992). The KfsTI values were moderately more variable than the KfsL ones and the means differed by a not statistically significant, and also negligible, 9% (Table 7). Moreover, the correlation between ln(KfsTI) and ln(KfsL) was statistically significant (Fig. 6) and the linear regression line did not differ significantly from the identity line, given that the 95% confidence intervals for the intercept and the slope were equal to −1.06–2.17 and 0.55–1.25, respectively. Therefore, this investigation showed that using a relatively complicated method to obtain a field measurement of α* did not modify significantly the Kfs predictions as compared with the ones obtained according to Elrick and Reynolds (1992), i.e. using a general description of soil characteristics. In other words, the simplified procedure developed by Bagarello et al. (2004) was supported by this analysis. The surface of the wetted area was found to be correlated with the α* parameter obtained with the TI in the − 30 to − 10 mm pressure head range (Fig. 7). In particular, α* decreased as ATI increased, which is physically plausible given that small wetted areas are expected in soils with large α* values, where flow processes are dominated by gravity (i.e., weak capillarity). Therefore, a possible strategy to obtain an estimate of α* representative for a particular location could be to locally establish a TI infiltration process at the highest possible pressure head, and then measure the size of the wetted area when the flow reaches apparent steadiness. Obviously, this procedure needs further testing and developments, also to support the applicability of the detected α* vs. ATI relationship with a TI experiment using a single pressure head, and in other soils.

V. Bagarello et al. / Geoderma 187–188 (2012) 49–58

Statistic

α*

KfsL

KfsTI

Minimum Maximum Geometric mean Coefficient of variation

4.8 44.6 16.3 0.60

21.3 635.1 92.3 a 1.16

12.2 740.7 100.5 a 1.46

Values in a row followed by the same lower case letter are not significantly different according to a two tailed paired t test at the P = 0.05 probability level.

5. Conclusions Different experiments were carried out with the general objective to assess the reliability of a field measurement of saturated soil hydraulic conductivity, Kfs, carried out by the Simplified Falling Head (SFH) technique. For a sampling campaign carried out in a relatively appreciable number of sites with both 0.15 and 0.30 m diam. rings, a significant ring size effect on the measured Kfs was detected. The Kfs values obtained with the large ring were found to be more reliable than the ones measured with the small ring since they were less variable and better correlated with other soil properties by physically convincing relationships. Ring size effects on the measured conductivity were particularly noticeable (discrepancy by more than an order of magnitude) in low permeability soils, and statistically significant relationships between the Kfs values obtained with rings differing in size were developed. These relationships have potentially a great applicative interest, since they suggested that a measurement carried out with a small ring contains enough information to make an approximate prediction of the Kfs value that would be obtained at the same site with a larger ring. Testing the developed relationships in other soils is clearly desirable. In a comparison between the SFH and single ring Pressure Infiltrometer (PI) techniques for a clay loam soil, similar means (i.e. not significantly different) but substantially different coefficients of variation (much higher for the SFH technique than the PI one) were obtained. The conclusion was that the two methods should be considered complementary, being usable to determine Kfs at the beginning (SFH) and at a later stage (PI) of a ponding infiltration process in an initially unsaturated, relatively fine textured, soil. Finally, using the tension infiltrometer (TI) method to measure in the field the α* parameter used in the saturated conductivity calculations did not modify significantly the Kfs predictions as compared with the ones obtained on the basis of a general description of soil characteristics, as originally suggested for the SFH technique. In

7 y = 0.8955x + 0.5578 R² = 0.6017

ln(KfsTI)

6 5 4 3 2 2

3

4

5

6

7

ln(KfsL) Fig. 6. Comparison between the field saturated hydraulic conductivity values obtained by using a literature estimate of the α* parameter, KfsL (mm h− 1), and a measurement of this parameter based on a tension infiltrometer experiment, KfsTI (mm h− 1) (sample size = 21).

50 y = 1.0666x-1.236 R² = 0.6148

40

α* (m-1)

Table 7 Summary statistics of the α* parameter (m− 1) obtained with the tension infiltrometer (TI) in the − 10 to − 30 mm pressure head range and the field saturated soil hydraulic conductivity, in mm h− 1, calculated by an α* parameter either taken from the literature (KfsL) or set equal to the one measured with the TI (KfsTI) (sample size, N = 21).

57

30 20 10 0 0.05

0.1

0.15

0.2

0.25

ATI(m2) Fig. 7. Relationship between the α* parameter determined with the tension infiltrometer experiment and the surface of the wetted area at the end of the unsaturated infiltration process, ATI (sample size = 21).

addition, the size of the wetted area at the soil surface immediately after a TI run may be used to obtain an approximate estimate of α*. In conclusion, this investigation gave support to the use of the SFH technique for a rapid and reasonably simple determination of the order of magnitude of Kfs. A feature of the technique that objectively limits its field use is the need to establish a one dimensional infiltration process during the test. This constraint imposes a relatively deep insertion of the ring into the soil, which determines a relatively high risk to disturb the soil, and also implies the need to preliminarily determine the volume of water to be used, to avoid the risk that the wetting front emerges from the bottom of the confined soil volume during infiltration of the applied water volume. Therefore, a future improvement of the technique will be aimed at developing a still simple analytical approach to the transient three‐dimensional flow process from a single ring inserted a short distance into the soil.

Acknowledgments This study was supported by grants of the Università degli Studi di Palermo (fondi ex 60%, Dottorato di Ricerca in Idronomia Ambientale) and the Sicilian Region (Progetti DIFA, CISS, MONIDS, Imera Meridionale). Thanks to G. Barone, M. Birtone, A. Giangrosso, S. Pomilla, S. Sferlazza, and A. Sgroi for their help in the experimental work. Vincenzo Bagarello and Massimo Iovino outlined the investigations. All authors contributed to analyze the data and write the manuscript.

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