Soil Science Society of America Journal 66:373-383 (2002)
© 2002 Soil Science Society of America
DIVISION S-1—SOIL PHYSICS
Using TDR to Estimate Hydraulic Conductivity and Air Entry in Growing Media and Sand
Jean Caron*,a,
Louis-Marie Rivièreb,
Sylvain Charpentierb,
Pierre Renaultc and
Jean-Charles Michelb
a Département des sols et de génie agroalimentaire, Université Laval, Sainte-Foy, QC, Canada G1K 7P4
b SAGAH-Institut national de la recherche agronomique, Centre d'Angers and Institut national d'horticulture, 42 Georges Morel, C.P.57, Beaucouzé 49071 France
c Unité de science du sol. – Domaine St-Paul – Site Agroparc Avignon, 84914 France
* Corresponding author (jean.caron{at}sga.ulaval.ca)
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ABSTRACT
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Gas relative diffusivity measurements are key indicators of the quality of growing media. Previous studies have shown that this property can be estimated indirectly from measurements of the point of air entry (
a), air-filled porosity (
a), and saturated hydraulic conductivity (Ks). Different tools are required to measure these parameters and this paper investigates how a single tool, time domain reflectrometry (TDR), already used to determine a from measurements of volumetric water content (), could be utilized to measure a and Ks in growing media. Cylinders were filled with 13 different substrates and coarse sand. A transient-state technique (vertical infiltration at -1 hPa of water potential) was used to calculate Ks from measurements in time. In growing media, calculated Ks values from transient-state experiment were statistically equal to estimates obtained from steady-state measurements at a potential of -1hPa. However, both methods underestimated the Ks values obtained under steady-state conditions after a pulse of water had been applied or after prolonged wetting. For sand, TDR-based measurements and steady-state infiltration at -1 hPa, provided estimates of Ks equal to those obtained after prolonged saturation. To estimate a, TDR probes in a horizontal and a vertical position were tested in addition to a pressure transducer technique. For growing media, the horizontal positioning of the probes provided more consistent estimates of a than the other two techniques. Estimates of a with TDR in sand, both in vertical and horizontal position, were similar.
Abbreviations: a, air-filled porosity • Ds/Do, gas relative diffusivity • a, point of air entry • , volumetric water content • Ks, saturated hydraulic conductivity • Kns, hydraulic conductivity near saturation • MWD, mean weight diameter • Pb, peat block treatment • PBc, coarse pine bark/blond peat, a 1:1 ratio, treatment • PPc, coarse blond peat/blond peat, 1:1 ratio, treatment • Rw, Rockwool slab treatment • Sc, coarse sand treatment • TDR, time domain reflectrometry
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INTRODUCTION
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THE AERATION PROPERTIES of artificial mixes used in horticulture are key characteristics to consider when manufacturing these mixes to ensure optimum crop yield. Gas relative diffusivity (Ds/Do), the ratio of the diffusion of a given gas in the soil relative to its diffusion in free air at a same temperature is one of these critical parameters characterizing aeration in growing media and well correlated to plant growth (Allaire et al., 1996; Caron and Nkongolo, 1999). Recently, Nkongolo (1996) showed that Ds/Do can be predicted with reasonable accuracy using routinely measured parameters such as a, Ks, and a, and efforts are made to investigate simple ways to estimate these parameters. Because the structure of artificial mixes is very sensitive to handling, such alternative methods must be carried out directly in pots (Paquet et al., 1993) and the development of noninvasive techniques like TDR may open the route to in situ characterization of Ks and a in pots with one single tool, as a can already be measured that way (Paquet et al., 1993).
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Measuring the Saturated Hydraulic Conductivity
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When using constant head permeameters to measure Ks under steady-state conditions in nursery or greenhouse pots with variable drainage hole distribution, the outflow configuration must be taken into account (Allaire et al., 1994). In such a case, Laplace's equation must be solved and a calibration experiment conducted to obtain an accurate Ks estimate, since the distribution of holes in the pot significantly affects Ks estimates (Allaire et al., 1994). With this same device, experimenters must also avoid inducing bypass flow, which may occur to potted substrates handled when wet. Indeed, the substrates deform when the pots change shape, but may remain deformed even after the pots have returned to their original shape, leaving a considerable gap along the pot walls. A gap may also appear along the pot walls as a result of substrate shrinkage. Since bypass flow introduces biases in Ks estimations, bentonite is applied along the walls to fill the gap. However, the effectiveness of this procedure remains unconfirmed.
Bypass flow can be avoided by applying a very high potential (close to saturation) to the substrate with a tension infiltrometer. However, for properly evaluating Ks, the applied tension must be maintained above the point of water entry (the point at which water enters the largest pores) to ensure maintaining conditions of saturation within the substrate itself, while bypassing large cracks along pot walls. The measurements must be carried out for a sufficient length of time so as to allow water entry into the micropores and the displacement of trapped gas molecules to ensure that the substrate is fully saturated.
However, as steady-state is reached soon after water drains at the bottom of the pot, the flux is then affected by outflow configuration. Instead, transient-state methods may be preferable for the evaluation of Ks during sorption, provided they are sufficiently accurate and ensure adequate saturation of the media. Indeed, as transient-state methods provide estimates of Ks before water flows from the bottom of the pot, they effectively eliminate the need to consider the effect of outflow configuration on Ks estimation. The accuracy of such methods has not been determined in growing media so far.
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Measuring the Point of Air Entry
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In mineral and artificial mixes, a is usually determined from the water desorption curve. However, the operation is delicate to perform and its accuracy can be limited by the rapid drainage that occurs when the substrates are handled close to saturation. Significant water loss occurs when the substrates or soils are displaced for weighing when a is close to zero water potential, or may also result from the shrinkage that occurs when a substrate structure that is loose at zero potential contracts appreciably as soon as a tension is applied. These losses sometimes make difficult the determination of a from the desorption curve (Nemati et al., 2002).
Alternatively, pressure transducer readings during drainage could be used (Renault et al. 1998) but investigation in substrates have been limited (Nemati et al., 2002). Additionally, a method based on TDR measurements performed under hydrostatic conditions could be used for a determination. Since TDR may be employed in procedures for measuring Ks and a in soils and potting media (Elrick et al., 1993, Paquet et al., 1993), the estimation of a with this same device could lead to a complete single-tool approach for the estimation of Ds/Do directly in pots. To estimate all these parameters from TDR readings, sorption and transport equations are first described in terms of measurements, adapted to the particular context of growing media contained in pots or cylinders.
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THEORY
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Measuring Saturated Hydraulic Conductivity Using Time Domain Reflectometry
Different approaches can be used to calculate Ks. In coarse-textured soils, a reasonable estimation of Ks can be obtained during sorption with the Green and Ampt approach (Gras, 1988). This approach considers that for ponded infiltration, the measured conductivity K is equal to Ks for potential higher than hf (Youngs et al., 1993). Certainly, this approach may be criticized. Indeed, ideally, we should use not a step function decrease of K(h) at potential lower than hf but rather, the real shape of the K(h)-h relationship. During ponded infiltration, such models have been proposed (Broadridge and White, 1988). However, as the shape of the K(h)-h function approaches that of sand or get even sharper, those models can be shown to be close or even equal to the Green and Ampt approach (Broadridge and White, 1988; Youngs et al., 1993). Despite numerous claims that the Green and Ampt approach may not work, this simplified model may give results as satisfactory with experimental data as those obtained with other models assuming different shapes of the K(h)-h (Youngs, 1988).
Consider a homogeneous substrate in a cylinder of length L, with the vertical position of the wetting front located, at time t, at the vertical coordinate x(t), with x = 0 set at the bottom of the column (Fig. 1a)
. The analytical solution for the one-dimensional vertical infiltration of a wetting front moving downwards from L under transient-state conditions is provided in Eq. [1]:
 | [1] |
where Ks is the hydraulic conductivity at saturation (i.e., if the water potential set at the top surface (ho) is above the point of water entry, complete saturation is assumed, and hf, the potential at the wetting front, is also higher than the point of water and the point of air entry), 
s is the measured water content at saturation, and i is the measured initial water content. The advantage of this technique is that it is possible to determine the position of the wetting front from TDR readings of at different times, 
, using the approach of Noborio et al. (1996) adapted to the context of a wetting front moving downward with x defined positive upward (Fig. 1):
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Fig. 1. Possible water content at different locations following wetting, (A) saturation and (B) drainage; t represents different times, x(t), the position of the wetting front at time t, L is the length of the column, and xa is the point of air entry.
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The result is a water content form of Eq. [1], where Ks and hf can be estimated using the least-square method for readings. While typically quadratic, the relationship between L - x(t) and time can sometimes become linear as time increases, as the second term in brackets in Eq. [1], grows slower than L - x(t) (Hillel, 1980). Equation [1] then tends towards:
 | [3] |
In the presence of a water potential near zero at the wetting front, which may occur when very large pores dominate the rewetting process, or because of a pneumatic potential, this same term becomes negligible as infiltration begins. Indeed, if the potential is high or air ahead of the wetting front is compressed inside the medium, then hf becomes close to h0. The 
term in Eq. [3] is then eliminated, resulting in a zero intercept regression line.
This transient-state approach is subject to a number of assumptions (constant Ks, homogenous medium, no entrapped air, form of the saturated-unsaturated hydraulic conductivity-potential (k[h]-h) relationship, adequate saturation achieved) that needed to be verified with growing media. Moreover, the conditions encountered in potted substrates (short probes, rapid infiltration, possible unstable wetting fronts) could limit the possibility of using TDR combined with a low tension infiltrometer to approximate Ks but these aspects have so far received no consideration.
Measuring Point of Air Entry Using Time Domain Reflectometry
After saturation and drainage of water from a potted medium, a capillary fringe extends from the thin water table at the bottom of the pot up to the point of air entry, located at xa (Fig. 1b). The distribution of water from the bottom to the top of the pot therefore corresponds to a water desorption curve, from saturation at the bottom of the pot to a potential equivalent to the substrate height in hectopascals at the upper surface of the substrate, and the average volumetric water content represents the container capacity (c). Topp et al. (1982) and Nadler et al. (1991) showed that the TDR reading provides an estimate of the mean water content along the length of the probe. Under these conditions, the TDR reading is a measurement of at each depth, (x), integrated over the whole probe length (or substrate height in the case of a potted substrate) and then averaged over the whole length. Mathematically, the average water content represents:
 | [4] |
Therefore, the volumetric water content measured by TDR in the pot at container capacity (c) is simply equal to the total equivalent height of water from saturation to the substrate height, divided by the total length of the probes (the area under the water desorption curve from saturation down to the potential equivalent to the substrate height, divided by the probe length) as shown in Eq. [4].
Standard water-desorption curves for different substrates have been described by Fonteno et al. (1981). The potential of these curves ranges from 0 to -100 hPa, with a very sharp decrease in occurring in the first 20 hPa, followed by very little change in from -20 to -100kPa. Fonteno et al. (1981) reported that a linear decrease between saturation and drainage accurately described the shape of the water desorption curve for the 0 to -20 hPa range (R2 between 0.81 and 0.99). If water desorption in a narrow range is assumed to be linear, this general shape of the water desorption curve can be used to estimate a from TDR readings. In short pots and in short cylinders (20 cm and less), the following representation can be assumed: 
= s from x = 0 to x < xa, and (x) drops linearly from s at xa to f at x = L as time tends toward 
(Fig. 1b). After saturation and drainage, the measurement of c (with TDR probes inserted from the bottom of the pot), assuming a desorption curve modeled as mentioned above and given Eq. [4], corresponds to:
 | [5] |
Since s and L are measured values, xa, the equivalent in centimeters of a expressed in hPa, can be calculated from Eq.[6], provided an estimate of f, f, is obtained:
 | [6] |
The accuracy to obtain f from TDR at the surface being limited, using such an approach would still require a gravimetric estimation of this value from the top substrate layer though.
It is therefore theoretically possible to obtain a complete but indirect estimation of gas diffusivity with TDR. For irrigation purposes in growing media, this represents a complementary role for TDR technology, which is already used to monitor , a and the electrical conductivity. The practical interest of this approach is obvious as one tool can be used in different procedures to provide an estimate of gas diffusivity directly in potted substrates, as long as probe access holes are made in the pot walls. However, the approach still requires further study as it relies on numerous assumptions that have not yet been verified in growing media. This study aimed at evaluating the limitations of an approach based almost solely on TDR for the characterization of Ks and a in different growing media and in pure sand.
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MATERIALS AND METHODS
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Sample Preparation
Polyvinyl Cl cylinders (9.5 cm in diam. by 30 cm high) were cut into two (upper and lower) adjoining parts of equal size with a nylon mesh taped over the bottom of the lower cylinder. The cylinders were filled with different mixes commonly used in greenhouse production. A pure sand was included to compare with a mineral soil. The mixtures were:- Rockwool slab (Rw).
- Coarse sand (Sc).
- Peat block (Pb), hand-cut from a blond sphagnum peat (H3 on the Von Post scale).
- Fine-wood fibers (Hortifibre, La Florentaise, Saint Mars du Desert, France) mixed with a fine blond sphagnum peat (H3 on the Von Post scale) in a 1:1 (vol./vol.) ratio (HFf).
- Coarse-wood fibers (Hortifibre) mixed with the same fine blond peat in a 1:1 ratio (HFc).
- Fine perlite (1–2 mm) mixed with the blond peat in a 1:1 ratio (PPIf).
- Coarse perlite (4–6 mm) mixed with the blond peat in a 1:1 ratio (PPIc).
- Loose fine coconut (Cocos nucifera L) fibers (Cf).
- Coarse pine bark (10–20 mm) mixed with the blond peat in a 1:1 ratio (PBc).
- Fine pine bark (2–4 mm) mixed with the blond peat in a 1:1 ratio (PBf).
- Coarse-blond peat (10–20 mm) (H3 on the Von Post scale) mixed with the blond peat in a 1:1 ratio (PPc).
- Coarse coconut fiber (10-20 mm) mixed with the blond peat in a 1:1 ratio (Cc).
- Fine blond peat (1–2 mm) (H3 on the Von Post scale) mixed with the blond peat in a 1:1 ratio (PPf).
- Medium-blond peat (4-6 mm) (H3 on the Von Post scale) mixed with the blond peat in a 1:1 ratio (PPm).
The cylinders were loosely filled with the different mixes and prewetted from the bottom for 3 to 4 d by raising the water level in a bath until it reached the top of the sample. The mixes were then allowed to equilibrate for 3 to 5 d. The samples were prepared in four replicates, one of which was used to calibrate the TDR probes and the three others for the Ks and a measurements.
The particle-size distribution of the air-dried samples was determined by manual (hand shaking) dry sieving. The sieving was performed for 1 min. on a nest of sieves with apertures measuring 40, 20, 10, 5, 2, 0.8, and 0.2 mm. Particle distribution was expressed on an oven-dry basis and the mean weight diameter (MWD) was calculated according to Kemper and Rosenau (1986) to estimate the average particle size. The ash content of the oven-dried material was determined from the loss of ignition material at 550 °C for 16 h. The fine-blond peat used in these mixes all came from the same batch. It was sieved through a 10-mm sieve and an average MWD of 2.44 mm.
Time Domain Reflectometry Calibration
Two types of TDR equipment were used. A Campbell CS-615 system (two probes, 3 mm in diam., 33 mm apart, cut to 150 mm long; Campbell Scientific, Logan, UT) and a Tektronix 1502-C system (Tektronix, Beaverton, OR), with three long parallel (3 mm in diam., 17 mm apart, cut to 150 mm long; Tektronix, Beaverton, OR) or short parallel probes (1.5 mm in diam., 15 mm apart, cut to 85 mm) were chosen. After being saturated for 3 to 4 d, the samples were drained and equilibrated at -50 hPa. The top portion of the samples was then removed and the height of the remaining portion adjusted to 15 cm by leveling off the excess substrate. The samples were then resaturated for 2 d. Height measurements were then taken with a ruler, and Ka measurements were taken by inserting 150-mm long probes (Campbell or Tektronix) into the different media (Topp et al., 1980). The samples were then equilibrated at container capacity (an average potential of -7.5 hPa), at -20 and -50 hPa by placing the samples on a tension table (Topp and Zebchuk, 1979). Additional drainage was induced by placing the bottom of the sample on a dry sheet of paper for 3 d, and a final measurement was then taken. Measurements of height and Ka at these additional potentials were performed as above, with the probes inserted into new holes each time. The weight of the samples was recorded for each series of measurements. The cylinders were then emptied, and the contents weighed and placed in aluminum dishes for oven drying at 105 °C for 2 d to determine the final mass.
Measurements
The Ks and a parameters were estimated from three sequential measurements carried out on the same sample (Fig. 2)
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Sequence A: Ks and a Measurements During a Sorption-Desorption Process
The 30-cm long samples were taken off the tension table, the upper 15-cm sections removed (the cylinders were cut in two and taped together a priori), and the lower section leveled across the top surface. The samples were attached to a stand (Fig. 3)
. An air-entry probe (Renault, 1998) was inserted through a 23-mm diam. hole located 75 mm (from its center) from the bottom of each cylinder, and was pushed about 1 cm into the cylinder (Fig. 3). Putty was applied around the air-entry probe to ensure that the contact between the probe and the wall was airtight, forcing air to enter at the surface of the substrate only. The CS615 probes were inserted vertically from below and a first reading, i, was taken (Fig. 2, A.1). Although the vertical insertion of the probes can induce macropore flow, it is in this position that the probe has maximum sensitivity for calculating Ks for a moving wetting front. A shallow layer (
5 mm) of contact sand was spread over the upper substrate surface and placed in contact with a -1 hPa tension infiltrometer which covered the whole exposed surface of the substrate. This tension was selected because this was the highest potential that could be achieved with a tension infiltrometer without encountering problems when handling the infiltrometer for measurements in pots. It provides the advantage of avoiding sidewalls effects and limits the risk of having flow along the probes. This potential was assumed to be above the point of water entry of all substrates, therefore still allowing estimation of Ks, despite the tension applied.
The readings were taken every 5 s, beginning slightly before the contact between the infiltrometer and the sand layer occurred and stopping as soon as the first drops of water were collected from underneath the sample (Fig. 2, A.2). The Ks was then calculated using Eq. [1] through [3] and the readings. After steady-state conditions had been reached on the infiltrometer (three constant water heights in a row), a second estimation of Ks was obtained, and a reading near saturation, s, was also taken (Fig. 2, A.3). A pulse of water was induced by allowing some air to enter the infiltrometer, and once steady-state conditions were again established, a third estimate of Ks was made from three consecutive constant water-height readings within the infiltrometer (Fig. 2, A.4). A water-content reading, , was also taken at this time (Fig. 2, A.4). Then, a second pulse of water was induced with the infiltrometer. To ensure the system was airtight, the pressure increase was monitored with the air pressure probe, which indicated higher than atmospheric pressures following the pulse induction. The infiltrometer was then removed. The suction within the column was measured every 0.1250 s as drainage occurred (Fig. 2, A.5). The value of a was calculated from the highest suction recorded before the probe returned to atmospheric pressure.
Sequence B: Point of Air-entry Measurements Only
Once drainage was completed in Sequence A, the probes were removed and the air pressure probe hole was sealed with tape. The samples were then rewetted overnight for another determination of a with the TDR probes inserted vertically or horizontally. Long three-rod TDR probes were inserted vertically from underneath, in the same two holes used previously with the CS-615 (plus a newly created hole) A reading of s was taken while the substrate remained saturated and underwater (Fig. 2 and 3, B.1). The long TDR probes were then removed and replaced by steel rods of the same diameter to avoid air entry through these holes. Still under water (except for the side of the cylinder from which the probes were inserted), the short three-rod TDR probes were pushed into the substrate in a final horizontal position (Fig. 3) and putty was placed around the probes to render the system airtight. The cylinders were then placed on a stand underwater and gradually raised above the water by 1-cm increments (Fig. 3, B.2) to establish different suctions. The TDR readings were recorded with the Tektronix 1502 C as equilibrium was reached. Measurements of Ka were performed for heights from 3 cm of water above the probe down to cylinder capacity (about -6 hPa). The a value was determined visually from this - curve when the first appreciable drop in Ka (and hence the readings) was noticed (Nemati et al., 2002). If air entry had not been reached at container capacity, a capillary mat was inserted underneath the sample and put in contact with the water level to further reduce the potential from -6 hPa to -9 hPa. The readings of Ka from the vertically inserted electrodes were then taken at container capacity to obtain c (Fig. 2, B.3). Meanwhile, a 1-cm sample was taken from the upper surface to determine f gravimetrically, converting it to a volumetric water content from the whole bulk density estimates obtained from the total-porosity readings (s) performed in Step B.1. The points of air entry with the vertically inserted electrodes were calculated using Eq. [6].
Statistical Analyses
Statistical analyses were performed using the SAS/Stat Package Release 6.12 (SAS Inst., Raleigh, NC). The comparisons of slope between regression lines were performed using the substrate x freq or substrate x 
interaction (Littell et al., 1991). The parameters in Eq. [1] and [3] were obtained by a least-square estimation using the Mathcad software Release 4 procedure (Mathsoft Inc., Cambridge, MA). Total porosity was compared by analysis of variance using the GLM procedure (SAS Inst., Raleigh, NC).
Because many of the materials used in this study were of a fibrous nature, probe insertion sometimes resulted in substrate displacement, which was noticed at the time of handling. The data for these cases were later discarded as they showed erratic behavior.
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RESULTS AND DISCUSSION
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Time Domain Reflectometry Calibration
Figure 4a
represents the calibration curves obtained for the different materials using the CS-615 probe. Differences of up to 0.20 m3 m-3 were observed for a same measured period, but no significant differences in the slope of the calibration curves (as reflected by a nonsignificant substrate x period term), or in the intercept (no significant substrate effect) were detected between substrates in the analysis of variance in Table 1. Consequently, a common linear regression slope was computed and yielded an R2 of 0.91.
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Fig. 4. Calibration curves obtained using (A) the CS-615 and (B) the Tektronix 1502-C instruments. Mineral refers to substrates with <0.20 kg kg-1 of organic matter content, and organic, with 0.20 kg kg-1 of organic matter content and more.
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Figure 4b represents the calibration curve obtained on the same sample with the Tektronix 1502-C apparatus. As reported by Topp and Reynolds (1998), and Da Sylva et al. (1998), the relationship between and was found to be essentially linear, and linear regressions between and were consequently performed. Table 1 shows that there were significant differences in intercepts between the substrates (substrate effect significant at P = 0.0001). Differences in slope were also significant at P = 0.10, as reflected by the substrate interaction term. These differences may result from bound water (Topp et al., 1980) since the substrates contained both mineral (rockwool and sand) and organic fractions. Because Paquet et al. (1993) used a common calibration line for substrates with more than 0.20 g g-1 of organic matter content, the substrates were divided into two subgroups according to whether they were of mineral or organic (more than 0.20 g g-1 of organic matter) composition. Regression equations were performed within these two subgroups, and further analyses of variance showed no significant differences between regression lines within the subgroups. Therefore, these two subgroups were maintained for further measurements of Ka with the Tektronix apparatus. The fitted regression lines for these two subgroups are shown in Fig. 4b.
Measurements
Sequence A: Ks Measurements
Figure 5
shows typical positions of the wetting front-time relationship obtained with the CS-615 for the Pb, PPc, and the Sc treatments. Equation [1] was fitted to most of the data (2/3) after the water content was transformed into the position of the wetting front using Eq. [2]. However, the quadratic component was weak in most cases and clearly absent for about 1/3 of the data, showing a typical zero-intercept straight-line relationship. In these cases, Eq. [3] with no intercept was fitted to generate Ks estimates.
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Fig. 5. Examples of the relationships obtained between the position of the wetting front [L-x (t)] and time.
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The absence of the quadratic component was not attributable to the presence of a pneumatic potential, as measurements conducted at the same time with the air-pressure probes in A.2 (Fig. 2), showed no significant increase in air pressure. Alternatively, this may not be because of a very high potential at the wetting front, possibly because of hydrophobicity. Michel (1998) showed that the two most hydrophobic materials (peat and bark) were typically hydrophilic at potentials > -1000 hPa. However, since the substrates in this study were equilibrated at -50 hPa prior to rewetting, this seems unlikely. Moreover, the curve would not be linear but rather would take on a quadratic shape, with a vertical asymptote instead of a horizontal one. The most likely possibility was that the point of water entry (the potential at which the macropores will resaturate) was very high, and far higher than the usual a, at -3.5 hPa (Allaire et al., 1996). In this case, the largest pores would control rewetting at very high water potentials, close to the set potential of -1 hPa. Meanwhile, the micropores, being of much smaller diameter, would rewet very slowly at a much lower water potential, but this second process would have little influence on the magnitude of the infiltration process, as it would involve a closed or relatively closed pore system (Hoag and Price, 1997). This is supported by the fact that infiltration in the Pb and the susbtrate made of coarse peat (PPc), two substrates made of blond Sphagnum peat, differed. Indeed, the infiltration curve for Pb (more compacted with few macropores) was typically quadratic, while that of the coarse peat mix, PPc, was typically linear.
The Ks estimates obtained with TDR under transient-state conditions (A.2) were closely correlated (R2 = 0.85) with the value measured with a tension infiltrometer under steady-state conditions in A.3 and were near the 1:1 slope (Fig. 6)
. Statistical analyses showed that the estimates obtained in A.2 (using the Green and Ampt approach) were not significantly different from those obtained under steady state in A.3, for all soils. This indicates that the modeling approach was adequate and that the transient-state technique with TDR adequately estimated Ks obtained at steady state in A.3. However, after application of a pulse of water and establishing steady-state conditions again (in A.4, Fig. 2), the determined Ks increased further (an increase of approximately five times) and showed a poor correlation (R2 = 0.31) with the measured infiltration under tension in A.3. (Fig. 6). Statistical analyses also showed that these estimates obtained in A.4 were significantly higher than those obtained in A.2 and A.3 for all substrates, but the coarse sand. Further investigation showed that if wetting was prolonged for 24 h and full saturation achieved, estimates of Ks would be statistically equal to those obtained in A.4 (data not shown). Therefore, the highest Ks values obtained were achieved with A.4, despite the fact that only a short pulse of water was applied at the surface of the samples tested and substrates remained unsaturated. This shows that Ks estimates could be characterized in pots, with a single-pulse application of water, before establishing steady state with a tension infiltrometer.
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Fig. 6. Relationship between the Ks estimates obtained under transient-state conditions with TDR (A.2), under steady-state conditions with an infiltrometer after a rapid resaturation with a pulse of water (A.4), under steady-state conditions with an infiltrometer after prolonged resaturation (B.1), and the Ks estimate obtained under steady-state conditions following wetting under tension (A.3).
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This also shows that in A.2 and A.3, an estimate of K near saturation (Kns) was obtained but for sand. This difference between A.2 and A.3 on one hand and A.4 on the other hand, was most likely because of hysteresis of growing media (Otten, 1994). Indeed, water contents (s) measured during the infiltration measurements in A.3 and A.4 (Fig. 2) increased by 0.10 m3 m-3 (from 0.66 to 0.76 m3 m-3) for nearly all treatments except the sand, which remained at 0.47 m3 m-3 (Table 2). Prolonged wetting for 24 h brought water contents to values usually observed for these growing media (0.80–0.90 cm-3 cm-3). The high value for sand most likely resulted from the fact that values of s obtained in A.2 and A.3 were measured with the CS-615 and that the use of a single calibration resulted in a lot of measurement errors associated with a single period reading (Fig. 4a). In B.1, empty space along probe might also be present, as those measurements were performed with the Tektronix 1502 C, more precise because it had two separate calibrations, and were also a bit high for sand.
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Table 2. Volumetric water content obtained following saturation under 1 hPa tension wetting (A.3), followed by a pulse of water (A.4), and drainage and overnight wetting (B.1).
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These results showed that despite cautious attempts to resaturate large pores were made, wetting at a potential as high as -1 hPa from above was insufficient for all media but sand. The results were somewhat unexpected as some of our preliminary work indicated rewetting would occur at potential lower than that value from below. Maybe this rewetting was far too slow relative to that occurring in larger pores. Nevertheless, Ks is likely to be underestimated if a pulse of water is not applied or if a tension instead of a pressure infiltrometer is used to perform flow measurements. On one hand, the results are promising as they indicated that transient methods may be used to estimate Ks and so, this allows the determination of Ks in pot with variable hole distribution without having to correct the flux density measurements for outflow configuration (Allaire et al., 1994). On the other hand, this indicated that tension wetting has to be avoided to ensure that all pores participating in fast transport are saturated for transient state conditions. Then, this indicates that constant pressure head infiltrometer should be used instead to maintain a constant height of water at the pot surface. This practically implies that with such device, precautions have to be taken to avoid sidewall effects when measuring Ks by putting bentonite along pot walls, adding a step to the measurement procedure. For s the results show that total porosity is underestimated when a pulse of water is induced without prior prolonged saturation of the growing media. Further work should investigate the effect of higher initial water content on the transient approach for measuring Ks and s.
The conclusions are different for the coarse sand. Whatever the estimation procedure (A.2, A.3, or A.4), the estimates were all equal, showing that the transient-state tension-wetting procedure provides an adequate evaluation of Ks (Fig. 6). This view also hold for total porosity measurements, where the coarse sand was the only treatment to show nonsignificant differences in volumetric water content for all procedures (A.3, A.4, and B.1).
Sequence A and B: Measurements of Point of Air Entry
The measurements obtained in A.5 with the pressure transducer in the sand, the Pb, the PPc, the Rw, and the PBc are shown in Fig. 7
. Following the pulse of water induced in A.4, a positive pressure was first observed. Then, once the tension infiltrometer was removed, the suction dropped down to the point where air entered the system. For a better visual representation, only the negative pressures recorded immediately following the removal of the tension infiltrometer are shown in the figure.
It should be noted, however, that for the sand and the compacted peat block, a was attained gradually with a return to atmospheric pressure occurring over 60 s (not shown). For coarse material, the drop in pressure often occurred at a rapid rate, which may be because of the fact that the pores involved in air entry were very large and therefore carried air bubbles which rapidly broke the water column. For some readings, it was not possible to obtain a estimates, possibly because of the frequency of measurements (one measurement every 0.1250 s). It is interesting that fluctuations were observed in the signals with these coarse media (Fig. 7). This is consistent with the concept of pores presenting bottlenecks where the water column breaks at high potentials, allowing air to enter the system, and then breaks again later as the potential drops further (Fig. 7, early points of the PPc curve). The fluctuations could also occur as a result of interconnected pore entered by air refilling through an interconnection with an expanded zone of larger pores suddenly exposed to air (curves for PPc and PBc). Finally, the fluctuations may also reflect a fragile substrate, where detached particles move during water movement, clogging some pores at specific locations. This would result in constrictions, which would lead to a decrease in the a value. Alternatively, the detachment of particles could lead to an increase in the point of air entry as suction increases.
The a was estimated visually from the curves and calculated as the minimum air pressure recorded following the water pulse. The point of air entry was also estimated in B.2 and from B.1 and B.3 (Eq. [6]) (TDR inserted vertically). Table 3 summarizes the a values obtained for the different substrates using the three different approaches, along with their mean values. Overall, there were significant differences between the methods (as reflected by the high F value for the method effect in the ANOVA). On average, a estimates were close to -3.5 hPa with the TDR probes inserted horizontally, -2.0 hPa with the pressure transducer and +1.1 hPa with the TDR probes inserted vertically.
There should also be an inverse relationship between particle MWD and a. The TDR estimates obtained with horizontal probe placement were the only ones that showed a significant relationship with MWD (R2 = 0.30). The TDR estimates with the probes in a vertical position had an R2 of 0.18, and the pressure transducer, an R2 of 0.00. The estimates obtained with the TDR probes inserted horizontally appear more realistic, however, as they were the closest estimates to those previously obtained by Allaire et al. (1996) and Nemati et al. (2002), and the method is similar to classical method of determining a from water desorption curve. Estimates for sand between methods were statistically equal. This suggests that vertical insertion of the probe may be adequate to estimate a in sand but inadequate in growing media.
Obviously, the a estimates obtained with the TDR probes inserted vertically in growing media are unrealistic, as at this potential, peat and bark are typically hydrophilic and therefore positive air-entry values are illogical (Michel, 1998). Different attempts were made to reduce the relatively high number of positive points of air entry obtained with TDR in vertical position, which values were physically impossible given the fact that the substrates were wetted under tension. The accuracy of the model and the solution given by Eq. [6] were checked in the third replicate by conducting a gravimetric estimation of s, c, and f. The insertion of these estimates into Eq. [6] eliminated all positive values and yielded an average a of -3.2 hPa (data not shown). This suggests that improving TDR accuracy would also improve the accuracy of the a estimation with the probes in a vertical position.
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CONCLUSIONS
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For growing media, results show that TDR readings during transient state vertical infiltration provided consistent estimates of Kns, and could be used to avoid having to consider outflow configuration effects in pots. However, for adequate Ks estimation, such substrates appeared too hysteretic to be characterized under low tension wetting. The measurement can still be performed rapidly though using steady-state infiltration, as a pulse of water is enough to obtain Ks values comparable with those obtained after 24 h of wetting. Results suggest that constant pressure head devices should be preferred to tension infiltrometer for use with transient-state techniques for measuring Ks. Consistent a estimates were obtained with TDR probes placed horizontally in growing media. Saturation induced with a pulse of water appeared insufficient to fully saturate media previously equilibrated at -50 hPa, and therefore also insufficient to adequately estimate s in growing media but in sand. For such growing media, prolonged wetting appears a must for substrates previously equilibrated at that potential.
These conclusions may be specific to growing media because of their particular nature. Indeed, in sand, tension wetting appears to provide an accurate estimation of Ks, as tension wetting and transient-state conditions provided estimates of Ks comparable with the estimates obtained under steady-state conditions with or without a pulse of water. In sand, the TDR probe inserted in a vertical position also appeared to provide a consistent estimate of a. Such a rapid characterization process could be used in sandy soils to estimate gas diffusivity from TDR readings alone, and should be evaluated for a wide range of sandy soils and air content.
Results on transient state infiltration are rather encouraging. Further work should investigate at which initial matrix potential and constant pressure head a transient-state approach could be used for in situ characterization of Ks. Additional work should be pursued also to check at which initial matrix potential complete saturation can be achieved with a constant head infiltrometer, for adequate s determination. Such steps appear important for eventually being able to perform measurements under transient state at the greenhouse or nursery scale, without having to immerse pots for 24 h, and using only a TDR and an infiltrometer.
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ACKNOWLEDGMENTS
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The authors thank Gilles Guillemain and Odile Douillet for their valuable assistance, France Chabot and Carmen Bilodeau for the typesetting, and Nicole De Rouin for reviewing the manuscript.
Received for publication January 24, 2001.
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