# Vadose Zone Journal

- Soil Science Society of America

## Abstract

Knowledge of gas exchange dynamics is important in determining the suitability of growing media used in nursery and greenhouse production. However, gas diffusion measurement methods are difficult to use directly in potted growing media and a rapid, simpler, and reliable approach appears desirable for routine assessment of gas diffusivity. This study compares gas diffusivity and pore efficiency estimates from gas diffusion chamber measurement with indirect estimates obtained from water storage and flow measurements and point of air entry values for various substrates. Four peat substrates with bark in variable particle sizes, a mineral soil, and silica sand were packed into aluminum cores in four replicates and then saturated for 72 h. After equilibration at −0.8 kPa of water potential on a tension table, the concentrations of N_{2} diffusing through these cores were measured in a gas diffusion chamber and gas diffusivity calculated from the gas concentration change in time. Diffusivity was also calculated with the water desorption curve and the saturated hydraulic conductivity, also measured on the same core (indirect approach). The gas diffusivity estimates obtained by gas diffusion chamber measurement were significantly correlated (*R*^{2} = 0.49, slope not different from 1) with those obtained from the indirect approach. Estimates obtained for pore efficiency were much closer and less variable than those for gas diffusivity (*R*^{2} = 0.80, slope not different from 1). The indirect approach may be a useful tool for the rapid assessment of gas exchange dynamics in growing media under undisturbed conditions.

In 1980, Topp and his coauthors published a paper dealing with the measurement of volumetric water content in mineral soils using time domain reflectometry (Topp et al., 1980). Showing that the technique could potentially be used in organic soils, the authors' results suggested the possibility of accurately and rapidly determining volumetric water content in growing media. Such a measurement has always been problematic because of the highly sensitive structure of growing media, which is greatly affected by potting procedures (Paquet et al., 1993; Heiskanen et al., 1996), root activity (Allaire-Leung et al., 1999), and container geometry (Bilderback and Fonteno, 1987), among other factors. Consequently, numerous studies have been conducted during the past 20 yr, focusing on TDR and capacitive methods for water content determination in peat (Pépin et al., 1991) and growing media (Paquet et al., 1993; Anisko et al., 1994; Lambiny et al., 1996; DaSylva et al., 1998; Murray et al., 2002). This opened the way to the complete in situ description of water storage and flow characteristics using TDR (Paquet et al., 1993; Caron et al., 2002; Murray et al. 2002; Nemati et al., 2002). These methods formed the basis for the in situ estimation of an empirical index of gas diffusivity first introduced by Allaire et al. (1996). Allaire et al. (1996), Nkongolo (1996), and Caron et al. (2001) then showed the relevance of using gas diffusivity (the ratio of gas diffusivity in the soil to that in free air) and pore efficiency (tortuosity) estimations obtained from water flow and storage characteristics in peat substrates as indices of plant growth to guide substrate manufacturing and diagnose plant growth problems in nursery or greenhouse applications. The accuracy of diffusivity and tortuosity in predicting plant growth suggested that such gas diffusivity estimations might be closely correlated with values obtained directly by diffusion chamber measurements.

## Gas Movement in Growing Media

Plant roots require oxygen to function normally. An insufficient supply of oxygen in soil pores impedes root respiration and stunts root growth, reducing water and nutrient uptake (Janick, 1986). Gases may also accumulate in soils, with deleterious effects on plant growth. As the soil oxygen is depleted and CO_{2} and ethylene gases accumulate, gaseous exchanges between the soil and the atmosphere above are required to replenish the soil's oxygen supply and eliminate the CO_{2} and ethylene.

Gaseous diffusion is the principal process involved in the gas exchange between the soil and the atmosphere (Taylor, 1949; Troeh et al., 1982), and the flux of a given gas can be described under steady state conditions by Fick's law: 1where *q* is the flux of gases, *D _{s}* is the effective gas diffusion coefficient and ∂

*C*/∂

*x*is the gas concentration gradient. The effective gas diffusivity through the soil,

*D*, can be related to its diffusivity in the air,

_{s}*D*, with several models (Xu et al., 1992).

_{o}*D*is obviously a function of air-filled porosity since O

_{s}_{2}and CO

_{2}usually diffuse much faster through the gaseous phase than through the liquid phase.

*D*

_{s}is also clearly a function of pore effectiveness (pore tortuosity, pore constriction and pore continuity). These factors are combined into one fitting parameter called the pore effectiveness coefficient, obtained for a given data set.

King and Smith (1987) showed that in peat substrates, the relationship between gas diffusivity (*D*_{s}), pore effectiveness (γ), the proportion of the total volume occupied by air called air-filled porosity (θ* _{a}*), and gas diffusivity in the air (

*D*) could be expressed as 2Since θ

_{o}*is far easier to measure than*

_{a}*D*

_{s}, the extensive research work conducted on aeration in peat-based growing media has focused almost exclusively on air storage characteristics (θ

*), with little attention given to soil gas exchange properties (Rivière and Caron, 2001). Some work has, however, focused on the oxygen diffusion rate (Paul and Lee, 1976; Bunt, 1991) and gas diffusivity (Gislerod, 1982; King and Smith, 1987).*

_{a}When growing media are manufactured for use in nursery or greenhouses, adequate aeration conditions are usually obtained by mixing organic wastes (Chong and Cline, 1993), wood bark (Nkongolo and Caron, 1999), and other raw materials (Penninck et al., 1984) of variable size and geometry with fine organic and mineral fractions (peat, mineral soil). The storage characteristics of a medium (water-holding capacity, air-filled porosity) depends on particle size distribution, but not necessarily on the shape of its particles. However, some of the materials used as amendments do create physical barriers because of their shape, which may affect the gas exchange dynamics within the medium (Nkongolo and Caron, 1999). Because gas exchange parameters cannot so far be predicted from particle size distribution (Nkongolo and Caron, 1999), direct in situ measurements need to be performed.

Existing methods for the measurement of gas diffusion in soil cores are difficult to use in potted media where disturbance induces changes in some of the physical properties (Paquet et al., 1993). They are also difficult to use by the practitioners where gas diffusion measurements are required to monitor the changes in growing media properties across time (Allaire-Leung et al., 1999) and after potting (Heiskanen et al., 1996). A rapid and reliable approach that does not disturb the substrate and that can be used by practitioners at the nursery or at the greenhouse is therefore needed to obtain estimates of the gas exchange dynamics in substrates. Water desorption curve and saturated hydraulic conductivity are commonly used to assess substrate performances (Milks et al., 1989; Paquet et al., 1993; Allaire et al., 1994). On the basis of the work of King and Smith (1987), Allaire et al. (1996) suggested that an indirect assessment of gas exchange dynamics could be obtained from measurements of the whole water desorption curve and saturated hydraulic conductivity, but the assessment that Allaire et al. (1996) made has yet to be validated. Moldrup et al. (1996)(2003) investigated the relationship between gas diffusivity and water desorption characteristics in mineral soils and found there was a good correlation between the measured gas diffusivity values and those predicted from water storage properties, as long as one single measured gas diffusivity value was available. Their findings suggest that properties related to water flow and storage in a porous medium could be used to predict gas diffusivity with reasonable accuracy. This paper addresses this question further with regard to artificial mixes used in nursery and greenhouses production.

## THEORY

### Tortuosity, Constriction, and Closed Pores in a Diffusive Process

In air-filled tortuous tubes of uniform radius, Ball (1981) showed that gas relative diffusivity, *D _{s}*/

*D*, is equal to 3where

_{o}*r*is the radius of the tubes in centimeters,

*L*is the apparent length,

_{s}*n*is the number of straight tubes present in the porous medium,

*A*is the cross section, and

*L*is the real length for diffusion in the pore in the process.

_{g}Since the air-filled porosity of the sample, θ* _{a}*, is equal to 4It can be shown that 5(Currie, 1960), where

*L*/

_{s}*L*is the true pore tortuosity factor for gas.

_{g}For *n* identical constricted tubes of *v* different radii *r _{i}*, Ball (1981) showed that: 6where

*l*is the length of pores of radius

_{gi}*r*. This expression remains valid as long as flow can occur through the constricted pores. Peat substrates are often composed of several components that are mixed to create macropores that drain easily at a very high water potential. The pores in the peat, however, are essentially closed because of the presence of hydrocysts (Puutsjärvi, 1976), and microporosity in peat can represent between 19 and 56% of the substrate volume (Moinereau et al., 1982, p. 15–79). Components like perlite, polystyrene, bark, and plant residues also have micropores that are partially or totally obstructed because of internal voids and plant structural remnants (Spomer, 1975; Gras, 1982, p. 79–127; Moinereau et al., 1982, p. 15–79).

_{i}A porous medium with macropores of radius *r*_{1} and micropores of radius *r*_{2}, which are partially or totally closed, can be considered as a medium with dual porosity: continuous nearly straight pores and closed pores. Indeed, if the internal porosity is almost completely isolated, then it corresponds to a case where the equivalent radii *r*_{2}* ≪ r*_{1}, and the diffusive process in such constricted pores can be shown to tend toward 0 (Eq. [6]). The constriction factor can therefore be disregarded in these media, as diffusion will depend entirely on the number of pores with very little constriction for gas diffusion, *n _{ag}*, instead of

*n*.

Under the assumption that pores are clogged when constrictions are present, and that diffusion occurs only in *n _{ag}* pores of large radius with no constriction, then Eq. [6] is reduced to Eq. [3] in unconstricted pores except that the number of pores available for gaseous diffusion,

*n*, differs from the total number of pores,

_{ag}*n*, of the same class since some pores are available for storage but not for diffusion.

Because θ* _{a}* is equal to the amount of air that will eventually replace the drained water from all equivalent

*n*pores, both unconstricted (

*n*) or partially occluded (

_{ag}*n − n*), then Eq. [3] can be rewritten in a modified form of Eq. [5] by making use of Eq. [4]: 7in which a pore-clogging factor,

_{ag}*n*/

_{ag}*n*, is introduced and in which pore constriction is modeled as clogged pores. Both the pore-clogging and tortuosity factors can be combined into a pore effectiveness coefficient, γ, and the relationship

*D*/

_{s}*D*− θ

_{o}*then takes the form of Eq. [2]. Eq. [7] is therefore equivalent to Eq. [5], with a pore-clogging factor for gas flow,*

_{a}*n*/

_{ag}*n*, and takes the same form as Eq. [17], provided by Freijer (1994) for a tortuous jointed tube model, with the difference that the pore-clogging factor is the pore constriction factor in Freijer's study. This modeling approach is mathematically equivalent to the conceptual model of Arah and Ball (1994) in which a proportion of the air-filled pores are closed (remote pores), equivalent to

*n*/

_{ag}*n*, and the unclosed (marginal and arterial) pores are functionally linked through a pore tortuosity factor, equivalent to

*L*/

_{s}*L*.

_{g}### Tortuosity, Constriction, and Closed Pores in a Convective Process

For a saturated porous medium with one particle size and tortuous pores of uniform radius, Ball (1981) showed that the intrinsic permeability *K* of *n* straight and parallel tubes could be calculated as follows: 8where *L _{w}* is the real length of the tubes involved in the water flow. Eq. [8] is equal to 9if θ, the volumetric water content, is replaced by Eq. [10]: 10The intrinsic permeability of sections of

*n*identical tubes of different

*v*radii joined at random and in series to form tortuous paths can be calculated by Eq. [18] (Ball, 1981) and modeled as: 11As in the case of diffusion, the flow will tend toward 0 in the presence of small constrictions under the previous assumption that

*r*

_{2}≪

*r*

_{1}. As a result, small pores render only

*n*tubes out of

_{aw}*n*available for flow. The flow in the

*n*tubes follows Eq. [8], while it tends to 0 in the constricted pores following Eq. [11]. Introducing Eq. [10] into Eq. [8], and replacing

_{aw}*n*by

*n*in Eq. [8] then yields 12which is an expression of the same form as Eq. [9] but includes the pore-clogging factor

_{aw}*n*/

_{aw}*n*. Hence, the unconstricted pore system can be considered as a special case of the constricted-clogged pore system for which

*n*/

_{aw}*n*= 1. The theory that follows addresses only the case of the constricted-clogged pore system.

For *m* classes of constricted-clogged pores of small radius, Eq. [12] can be extended to 13where (Δθ)* _{j}* is the volumetric water content (in cm

^{3}cm

^{−3}) of pores with a mean radius of

*r*in the class

_{j}*j*.

Under the assumption that *n _{awj}*/

*n*and

_{j}*L*/

_{s}*L*are constant coefficients across the

_{wj}*m*classes of pores (capable of sorbing water within a given range of water potentials), and given the fact that the radius of micropores is much smaller that that of macropores

*r*

_{2}<<<

*r*

_{1}: 14The same extension can be applied to diffusion where 15

Again, if these coefficients are assumed to be constant, then the pore effectiveness coefficient is constant across *m* classes of pores, a linear relationship between *D _{s}*/

*D*and θ

_{o}*in the form of Eq. [7] is obtained. This relationship pertains to peat substrates (King and Smith, 1987) and across short values of θ*

_{a}*in mineral soils (Bakker and Hidding, 1970) and peat substrates (Gislerod, 1982). Such a relationship has also been reported across a wide range of θ*

_{a}*in sand (Shimamura, 1992).*

_{a}On the basis of this theoretical approach and on an assumed pore organization supported by previous authors, the diffusive and the convective processes have similarities due to the geometry of the pore system in growing media. Its validity in sand remains unlikely though (see below). It is also observed that both these transport processes in a micro–macropore system are affected to the same extent by similar coefficients.

The intrinsic permeability, as calculated with Eq. [14] is independent of any fluid. In the case of water, the permeability, or saturated hydraulic conductivity, *K _{s}*, is equal to 16where

*K*units are in centimeters per second, η is the water viscosity (Pa s), ρ is the water density (g cm

_{s}^{−3}),

*g*is the acceleration due to gravity (m s

^{−2}), τ

*is the pore effectiveness coefficient for water flow, and the factor 10 is a unit conversion factor. The factor τ*

_{w}*is therefore a unitless weighting coefficient that takes into account both the dead-end pores that are not involved in transport and the fact that the real pathway for water flow is longer than the apparent one (Koorevaar et al., 1983). Its inverse represents a constant similar to (*

_{w}*L*/

_{s}*L*)

_{w}^{2}(

*n*/

_{aw}*n*) in Eq. [14].

However, this constant is theoretically not equal to the weighting coefficient (*L _{s}*/

*L*)

_{g}^{2}(

*n*/

_{ag}*n*) in Eq. [7]. Indeed, the pore effectiveness coefficients for water flow and for gas diffusion may be very different, as at high and moderately high water contents air may be trapped in large pores that are connected to small pores filled with water that block gas diffusion (Schjønning et al., 2002). However, following the assumption made earlier that the pore system is either severely constricted or unconstrained because of a bimodal (macropore–micropore) pore space, the pores filled with a film of water will severely limit diffusion and block water flow (Hoag and Price, 1997; Loxham, 1980). Under this assumption, the proportion of blocked pores for water,

*n*/

_{aw}*n*, is then identical to that for gas,

*n*/

_{ag}*n.*For

*L*/

_{s}*L*and

_{w}*L*/

_{s}*L*, important disparities may occur because diffusive processes obey a random walk process while convective velocity conforms to a well-organized pattern following Poiseuille's law (Hillel, 1980). Therefore, real lengths should theoretically differ for both processes. However, these disparities may have little effect if the

_{g}*n*/

_{ag}*n*ratio dominates the pore effectiveness coefficient. This is a critical point. Data from Hoag and Price (1997) and observations by Loxham (1980) suggest that a large number of pores are not connected for water flow. This in turn suggests that the low pore efficiency reported by King and Smith (1987) for peat relative to values reported for mineral soils (Gliński and Stępniewski, 1985) is dominated by a low

_{w}*n*/

_{ag}*n*ratio. Under such circumstances, the pore efficiency coefficients for both convective and diffusive processes tend to be very similar and the estimation of the pore efficiency coefficient for gas using water flow and storage becomes unbiased within a certain pore range. This implies that in such substrates 17Practically, this means that the γ in gas transport (Eq. [2]) can be estimated using a water flow experiment, as indeed 18and that the estimation is unbiased. However, an independent verification of this assumption is required.

_{w}The theory of the two methods of estimation of γ through water flow experiments is presented below. The first method is based on a complete estimation of the contribution of the different pores sizes to water flow by measuring the whole water desorption curve (multiple-point method). The second method is based on an estimation of this contribution using only two points of the water desorption curve (two-point method).

### Multiple-Point Method

Van Genuchten and Nielsen (1985) developed a nonlinear, five-parameter function to describe the water desorption curve of soils. This function was adapted to horticultural substrates by Milks et al. (1989) as follows: 19where θ = *F*(ψ, θ* _{r}, n, b,* α) and θ

*is the mean volumetric water content of the soil at saturation (total porosity), θ*

_{s}*is the mean volumetric water content at asymptotic residual, ψ is the water potential (kPa), and*

_{r}*b*,

*n*, and α are empirically fitted iterated parameters. By rearrangement and by the use of a dimensionless water content, 20

Solving Eq. [19] for ψ yields, 21On the basis of the principles of capillary rise (Hillel, 1980), it is known that: 22where *r* is the pore radius in centimeters, σ is the surface tension of water, and ε is the wetting angle formed between the air, the water, and the soil surfaces. The expression is reasonably well approximated by the right hand side of Eq. [22] if *r* is expressed in centimeters and the wetting period is sufficiently long for the wetting angle to be 0. The conversion factor, 0.03, then has the unit of kilopascal centimeters. Combining Eq. [21] and Eq. [22] generates 23By solving for *r* and squaring each side of the equation, the expression becomes: 24where *r* is computable for *m* classes of pores containing a differential volumetric water content using the parameters of the water desorption curve of a substrate. Eq. [16] is rewritten in a summation form. However, an integral form can be taken as the water content-*r ^{2}* function can be described by Eq. [24]. Substituting

*r*

^{2}with the right hand side of Eq. [24] and isolating τ

*, 25where the upper limit of the integral is calculated from the volumetric water content at the point of air entry, θ*

_{w}*, as this upper limit will correspond to the radius of the largest pore involved in water flow. The lower limit, θ*

_{ea}*, is calculated from the residual water content at a water potential of −10 kPa. Although the lower limit should theoretically be 0, the contribution to*

_{r}*K*of pores retaining water at water potentials lower than −10 kPa in peat substrates is so small that it is considered to be negligible and can be disregarded for τ

_{s}*calculations. As information on α,*

_{w}*b*, and

*n*relationship is obtained from the water desorption curve and

*K*is determined from a direct measurement, τ

_{s}*can be calculated from Eq. [25]. Relative gas diffusivity (*

_{w}*D*/

_{s}*D*) can be obtained from Eq. [18] by simply dividing air-filled porosity by τ

_{o}*. This estimation of*

_{w}*D*/

_{s}*D*may be biased, however, if the assumptions made earlier are not valid. The

_{o}*D*/

_{s}*D*parameter can therefore be used as an index of the gas exchange dynamics in substrates by simply measuring

_{o}*K*and water retention in pots. Since methods for measuring

_{s}*K*and the ψ–θ relationship directly in pots under undisturbed conditions are now available (Paquet et al., 1993; Allaire et al., 1994),

_{s}*D*/

_{s}*D*can therefore be obtained directly in potted media of variable geometry without disturbing the substrate.

_{o}For applications in the laboratory, it is particularly appropriate as these properties are usually measured for quality control purposes. However, for a quick diagnosis in nursery or greenhouses applications, the proposed method is time-consuming as it requires that the entire water desorption curve be determined. Moreover, the numerical integration of Eq. [25] is required, and although this operation can be performed using commercially available software, it may present an additional limit to use such a method on a routine basis. A second method, a faster and simpler procedure, is therefore proposed.

### Two-Point Method

The principle of this approach is that the early phase (from air entry to approximately −1 kPa) of water desorption in a peat substrate can be considered linear (see discussion below) and is represented by the following linear equation: 26Since this equation represents a straight line, only two points are required to determine the slope: β_{1} and the intercept β_{0}. If these two points can be determined between saturation and container capacity, a quick estimation of τ* _{w}* can be obtained as the drainage rate of these substrates is extremely rapid. Isolating ψ in Eq. [26], and replacing ψ in Eq. [22] by its equivalent expression, then isolating

*r*and squaring both sides of the resulting equation yields 27Again, rewriting Eq. [16] into an integral form, substituting the right hand side of Eq. [27] to

*r*yields 28Evaluating the integral in Eq. [28] then yields 29Expressing Eq. [29] in a potential form, after replacing the upper and lower limits in Eq. [28] and simplifying the expression, the equation becomes 30where ψ

^{2}*is the potential at air entry (i.e., at the point θ = θ*

_{a}*) and ψ*

_{ea}*is the potential at which θ*

_{r}*is reached. To estimate τ*

_{r}*(and subsequently*

_{w}*D*/

_{s}*D*from Eq. [2]), four unknown values must be determined: β

_{o}_{1}, θ

*, θ*

_{ea}*, and*

_{c}*K*.

_{s}*K*is obtained directly from water flow measurements. The value of β

_{s}_{1}, which is the slope of the linear regression line between ψ and θ (early phase of the water desorption curve), is obtained from two points: θ at the point of air entry (θ

*ψ*

_{ea,}*) and θ and ψ after saturation and drainage (θ*

_{a}

_{c}_{,}ψ

*). Since it is established that after saturation and drainage, substrates in cylinders will equilibrate at a potential (in centimeters) that is generally close to half the height of the substrate in the cylinder (Bilderback and Fonteno, 1987), ψ*

_{c}*need not be measured, but can be considered to be equal to half the height of the substrate in the cylinder (in negative value though, as indeed, after saturation and drainage, the potential at the bottom of the top equals zero and equals to minus the height [in centimeters], at the top of the substrate, for an average potential equals to half the height, if the pot form is a cylinder and if the substrate fills the pot to the top. The value can then be transformed into kilopascals). Moreover, in that case, θ*

_{c}*is calculated from θ*

_{ea}*(practically, a drop of about 0.02 cm*

_{s}^{3}cm

^{−3}relative to θ

*is observed as a result of shrinkage, before air entry). Since θ*

_{s}*and θ*

_{s}*can be easily measured with TDR, and ψ*

_{c}*estimated from the cylinder height, the only remaining unknown is ψ*

_{c}*. This can be estimated to be around −0.35 kPa, on the basis of data in literature (Allaire et al., 1996, Caron et al. 2002), measured in situ with TDR (Nemati et al., 2002), measured with a pressure transducer (Nemati et al., 2002), or estimated from the early part of the desorption curve. Consequently, β*

_{a}_{1}can be calculated as follows: 31Equation [30] can then be solved by using Eq. [26] to calculate ψ

*, since β*

_{r}_{1}and β

_{0}are known and θ

*is approximately 0.35 to 0.40 cm*

_{r}^{3}cm

^{−3}in peat substrates (Puutsjärvi, 1976; Moinereau et al., 1982, p. 15–79; Paquet et al., 1993). A different value of θ

*can be chosen when growing media having a lower θ*

_{r}*than peat are chosen (e.g., for sawdust and coarse bark, 0.15–0.20 cm*

_{r}^{3}cm

^{−3}may be more appropriate). Since

*K*, θ

_{s}*, θ*

_{s}*, and ψ*

_{c}*are measurable in situ and ψ*

_{a}_{r}can be calculated from β

_{1}and β

_{0}, it is therefore possible to use the two-point method to estimate τ

*. This method is considerably less time-consuming than the multiple-point method, since θ*

_{w}*in peat substrates is reached within 2 h (Puutsjärvi, 1968), all of the parameters can be obtained rapidly from substrate measurements, and calculations can be performed by hand with Eq. [30]. Such method gains considerably in time and practicality, but is expected to decrease precision in estimating τ*

_{c}*as it is assumed that the water desorption curve is linear.*

_{w}There is, therefore, theoretical basis for the belief that a reliable, unbiased estimation of γ, and consequently gas diffusivity, can be obtained from water flow and storage properties in growing media. However, the reliability of this estimation rests upon many assumptions. The objective of this paper is to determine if accurate estimates of gas diffusivity in peat substrates can be obtained from water flow and storage measurements.

## MATERIALS AND METHODS

### Sample Preparation

Four peat-based substrates, a mineral soil (sandy soil), and a silica sand were used in this experiment. The peat substrates were composed of 50% peat, 40% bark, and 10% sand (volume basis, Table 1). Peat and sand particle size remained constant while bark particle size varied: 1 to 2, 2 to 4, 4 to 8, and 8 to 16 mm (Table 2). The substrates, the soil, and the silica sand were poured (without compaction) into aluminum cylinders measuring 9.8 cm in diameter and 10.1 cm in height and overfilled above the top surface of the cylinder. The bottoms of the cylinders were covered with an aluminum wire mesh to retain the soil, the silica sand, and the peat substrates. Nine tension tables were prepared in advance in the laboratory. A tensiometer was inserted into each tension table to monitor the water potential. The cylinders were saturated for 72 h and transferred onto tension tables (Topp and Zebchuk, 1979) for equilibration at −0.8 kPa of water potential. Wet substrate was added to the core to compensate for shrinkage when necessary, before equilibration. The cores were then transferred one by one onto the diffusion chamber. Four replications of the six substrates were used in this experiment yielding a total of 24 experimental units.

### Gas Diffusion Chamber Measurements

The experimental procedure followed was the same as that described by Xu et al. (1992). It consisted in measuring the concentration of N_{2} diffusing through the substrate cores in a gas diffusion chamber. The gas diffusion apparatus, constructed in plexiglass, was based on the design suggested by Rolston (1986) and adapted by Xu et al. (1992). The chamber was made as in Fig. 1 from Xu et al. (1992). Two rubber O-rings, one at the top of the base plate in a slot around the opening and the other immediately underneath the soil core, were used for sealing purposes. A tank of compressed gas containing a mixture of 80% Ar and 20% N_{2} was used to fill the diffusion chamber and to establish the initial gas concentration of the diffusion experiment. A gas chromatograph (Model 5890 Series II) was used to analyze the concentration of N_{2} in the diffusion chamber. The room temperature during the experiment varied from 21 to 23°C with a mean value of 22°C. A 5-mL gas sample was taken with a 6-mL syringe at 0, 3, 10, 20, 30, 40, 50, 60, 75, and 90 min after the start of the experiment. The gas sample was injected directly into the gas chromatograph. Then, from N_{2} concentration in the chamber *C*, a plot of ln[(*C* − *C _{s}*/(

*C*−

_{0}*C*)] vs. time was drawn, where

_{s}*C*is the gas concentration in the atmosphere and

_{s}*C*the initial concentration within the chamber. A linear regression was run from those data points within the linear part of the plot. As the slope of this line corresponded to −

_{0}*D*α

_{s}*/θ*

^{2}*, the value of*

_{a}*D*was calculated from the value of α found in Table 46-1 from Rolston (1986) and the θ

_{s}*obtained on the cores (see below).*

_{a}### Water Desorption Curve and Water Flow Characteristics

Following the gas diffusivity measurements, the same cores were used to measure *K _{s}*, θ

*, θ*

_{s}*, ψ*

_{c}*, and the entire desorption curve. Saturated hydraulic conductivity was measured with the constant head device with a constant head permeameter to maintain a constant water height at the top of the core (Klute and Dirksen, 1986).*

_{a}To measure θ* _{s}*, the cores were resaturated from underneath and time domain reflectometry (TDR) probes (12 cm long) were inserted at an angle of 35° from the vertical (to obtain complete insertion of the probes) to measure the dielectric constant (

*k*) according to the procedure of Topp et al. (1980). For peat substrates, the measured

_{a}*k*was converted into volumetric water content, θ, as follows (Paquet et al., 1993): 32for

_{a}*k*between 5 and 58. For

_{a}*k*values between 58 and 81, θ was interpolated from the value of θ at

_{a}*k*= 58 (computed with Eq. [32]) and a θ value of 1.00 cm

_{a}^{3}cm

^{−3}for

*k*= 81. For the mineral soil and the silica sand, the following relation was used (Topp et al., 1980): 33The first θ determination at saturation was used to estimate θ

_{a}*. Thereafter, the peat substrates, the mineral soil, and the silica sand cores were saturated and returned to the tension table to measure the water desorption curve from −0.8 kPa to −10 kPa. The first reading at −0.8 kPa was considered to correspond to container capacity, as such substrates were characterized for research on nursery and on 5-, 9-, and 13-L nursery pots. This potential of −0.8 kPa corresponds approximately to the potential measured at midsubstrate height in such nursery pots after saturation and drainage.*

_{s}Air-filled porosity (θ* _{a}*) was calculated from 34

### Air Entry Estimates

Measurements of the air entry values (ψ* _{a}*) were conducted separately from the water desorption curves since, in this case, the TDR probes needed to be inserted horizontally for increased accuracy. Cylindrical pots were filled, saturated, and equilibrated in the same manner as the cylinders. A TDR probe was then inserted horizontally through the side of the pot and the pot was inserted into a bucket. The water level was increased gradually up to rim of the pot and then lowered by 1-cm intervals as the changes in the water content were monitored. The point of air entry was considered to be where the first important drop in water content occurred as the water potential decreased. This determination procedure is described fully by Nemati et al. (2002).

### Gas Diffusivity Estimates

For the multiple-point method, pore tortuosity was calculated from Eq. [25] using Mathcad 2000 (MathSoft Inc., Cambridge, MA) to fit the water desorption data points. Once τ_{w} was obtained, Eq. [18] was used to calculate diffusivity from θ* _{a}* determined on the same core. For the two-point method, τ

*was obtained from Eq. [30], and diffusivity again with Eq. [18] and θ*

_{w}*determined on the same core.*

_{a}### Statistical Analysis

Substrate comparisons were performed by ANOVA for each individual method. The methods were also compared by ANOVA despite the restrictions to randomization imposed by the procedure. The interpretation was modified accordingly (see below). Comparisons between methods were also made using a regression analysis. Both the regression analysis and the ANOVA were performed using the SAS statistical package software Version 8.2 (SAS Institute, Cary, NC).

## RESULTS AND DISCUSSION

### Water Desorption Curves and Water Flow Characteristics

Major differences were observed between the substrates. Total porosity and air-filled porosity at −0.8 kPa were lower in the silica sand and the mineral soil than in the peat substrates (Fig. 1 and Table 3). The *K _{s}* values, however, were of the same order of magnitude in all substrates, indicating that the pore network is more efficient in the mineral soil and the silica sand than in the peat substrates for a same water-filled porosity. Varying the size of the bark particles in the peat substrates did not change either the total or the air-filled porosity, but the saturated hydraulic conductivity decreased significantly with increasing bark size, a finding that has been reported previously and investigated in detail (Nkongolo and Caron, 1999).

### Gas Diffusion Coefficient

In both the mineral soil and the silica sand, the three methods for measuring the relative gas diffusivity coefficient (*D _{s}*/

*D*) provided values in the same range (Table 4), and the estimates were consistent with the measurements found in the literature.

_{o}At a similar water content, estimates of *D _{s}*/

*D*for peat substrates varied between 0.007 and 0.0265 cm

_{o}^{2}s

^{−1}cm

^{−2}s (Fig. 2) , consistent with the

*D*/

_{s}*D*mean values ranging from 0.00025 to 0.0239 cm

_{o}^{2}s

^{−1}cm

^{−2}s found by King and Smith (1987) at similar θ

*. The estimates obtained here are also in agreement with the values reported by Gislerod (1982), which ranged between 0.005 and 0.04 at a volumetric water content between 0.02 and 0.30 cm*

_{a}^{3}cm

^{−3}(Fig. 2).

The *D _{s}*/

*D*coefficients for the silica sand and the mineral soil were higher than those for the D4-8 and D8-16 substrates despite the fact that air-filled porosity was much greater in the peat substrates (Table 4). This difference is most likely because of the fact that peat substrates are made of a fibrous matrix that can greatly increase the tortuosity in comparison with a granular material (Loxham, 1980; King and Smith, 1987). Also, as pointed out in the theoretical development, peat contains a large number of small pores called hydrocysts, which are closed or nearly closed, and these constrictions can severely impede water flow and remain filled with water because of their small openings measuring between 14 to 36 μm (Puutsjärvi, 1976). They therefore will restrict both the water flow and the gas diffusion despite providing a high porosity.

_{o}All three methods (gas diffusion chamber measurements, multiple- and two-point) confirmed the influence of the bark particle size on substrate properties (Table 4). Gas diffusion chamber measurements showed that gas relative diffusivity decreased linearly with increasing wood bark particle size, in keeping with the results of previous studies that showed that large bark fragments may create a barrier to gaseous diffusion (Nkongolo and Caron, 1999).

The mean value of the estimates for *D _{s}*/

*D*obtained with gas diffusion chamber measurements and the multiple-point method were comparable, while the mean obtained with the two-point method was significantly lower (Table 4). The restriction to randomization (the fact that gas diffusivity was always measured first by the diffusion chamber) normally should tend to decrease pore efficiency because of compaction and particle reorganization. However, no significant drop in substrate height was observed between gas diffusion chamber measurements and the measurement of water content at −0.8 kPa after resaturation, suggesting that restriction to randomization had negligible impact on the conclusions when comparing methods. When substrate differences were analyzed separately though, substrate effects were revealed with both the multiple-point and the two-point methods. The main difference in the results was that the trend for the 1- to 2- and 2- to 4-mm bark particles was reversed (differences were not significant, however) with these methods relative to the gas diffusion chamber measurements. Moreover, both indirect methods showed significant differences between the 2- to 4- and the 4- to 8-mm bark particles while none were detected with gas diffusion chamber measurements. All three methods had a similar CV value around 30%, with small but significant differences between the methods in ordering and discriminating substrates.

_{o}The results obtained by gas diffusion chamber measurements were correlated with the results from the other two methods (Fig. 3) . The correlations were significant for both the multiple- and the two-point methods, although the multiple-point method was more closely correlated to gas diffusion chamber measurements. The correlation coefficient remained low relative to the data obtained by Moldrup et al. (1996)(2003) in mineral soils. The low correlation can be attributed to both measurement techniques and the calculation methods. Indeed, for the indirect calculation approach presented in this study, diffusivity calculations are based on three estimations (instead of one for the diffusion chamber): air entry, *K _{s}*, and θ

*, all of which contain measurement errors in addition to the assumptions that are required. It was therefore expected that the calculated estimates from the water desorption curve would be less accurate than the gas diffusion chamber measurements. Another error may result from the fact that the water desorption curve data was obtained with the probe inserted into the substrate at an angle rather than horizontally, for practical reasons. While this obviously provides a more realistic estimation of θ*

_{a}*and θ*

_{a}*, it also introduces some error in the estimation of water desorption, which then worsens when the slope of the water desorption curve is estimated from only two points.*

_{c}With the two-point method, additional lack of fit may come from the fact that the water desorption curve was assumed to be linear for the 0 to −0.8 kPa range and the residual water content was extrapolated for the −0.8 to −2 kPa interval (see Fig. 1). While this is a reasonable assumption for peat substrates (Fonteno et al., 1981), it may be erroneous for sandy soils, as their water desorption curves show small drop in water content relative to peat substrates at high potential and is not linear within that range (Fig. 1). This may result in more errors in the estimation of β_{1} in Eq. [31], and therefore in errors in *D _{s}*/

*D*estimations by Eq. [30] and [18]. Finally, the lack of correlation for both methods with diffusion chamber may be because of the fact that the assumed hypothesized model does not hold (either for Eq. [17], Eq. [18], or both Eq. [17] and [18]). However, for peat substrates, this can only partially explain the lack of correlation for diffusivity (see below).

_{o}### Pore Effectiveness Coefficient

The γ values varied from 0.06 to 0.53, depending on the substrate (Table 4). The estimates for sand were consistent to those obtained by Shimamura (1992), but were slightly higher than those (1.0 to 0.74), probably because the model used by Shimamura (1992) to estimate γ differed from Eq. [18]. King and Smith (1987) obtained estimates around 0.14 for the pore effectiveness coefficient in peat for air-filled porosities between 0.05 to 0.26 cm^{3} cm^{−3}. Data from Table 1 in Hoag and Price (1997) yield a ratio of *n _{aw}*/

*n*between 0.16 and 0.43, and therefore similar γ values if (

*L*/

_{s}*L*)

_{w}^{2}is taken equal to 1. Therefore, the γ estimates in peat substrates were consistent with the data found in the literature.

Increasing the bark particle size decreased γ, consistent with previous findings (Nkongolo and Caron, 1999). The statistical analysis revealed pronounced substrate effects, and the γ values of the peat substrates were much lower than those of the mineral soil or the silica sand. The analysis also revealed the presence of a nearly significant method effect (*P* = 0.072), attributable mainly to higher γ values for the two-point method than for the multiple-point or gas diffusion chamber measurements approaches (Table 4). Compared with the gas diffusion chamber measurements results, the γ estimates for peat bark mixes obtained with the multiple or two-point desorption curve showed apparent inconsistencies. Indeed, values for the D1-2 bark were lower than those for the D2-4, and values for the D4-8 were higher than those for the D8-16, which was unexpected. Although these differences were not significant, they indicate that the multiple- and two-point methods are less accurate than the diffusion chamber technique.

The calculated γ estimates were, however, in general more accurate than the gas diffusivity estimates because of the higher correlation coefficient for the two methods with the diffusion chamber method (Fig. 4) . The correlation for the γ estimates with the different methods indicates that the estimates obtained with the multiple-point approach become more variable as γ increases, that is, as the γ estimates corresponded to mineral soils (Fig. 4). This is probably because of the fact that the modeling approach used to characterize the water desorption curve in peat substrates, from which τ* _{w}* (and then γ) is calculated, may induce error when used for mineral soils (see above discussion). The slope tends to be biased (tends to depart from the 1:1 slope, despite that the slope was not significantly different from the 1:1 slope) when measurements are performed on mineral soils, which suggests that the assumptions made earlier for peat substrates may not be valid in mineral soils or in substrates with a high proportion of sand.

The CV was lowest for gas diffusion chamber measurements and highest for the two-point method, but the differences were small. Nevertheless, the observed variability suggests that multiple measurements are needed to obtain a more accurate estimation and effectively, variability was largely reduced when mean values were compared. Indeed, when mean values were compared, the *R*^{2} of the correlation between the multiple-point method and diffusion chamber measurements increased to 0.93 and the slope was not significantly different from 1, indicating no bias (data not shown).

The absence of bias with the multiple point method may be because of the fact that it is not the *L _{s}*/

*L*ratio in Eq. [8] that governs τ

_{g}*or γ, but rather the*

_{w}*n*/

_{ag}*n*parameter. As this ratio was shown in theory to be equal for pore convective and diffusive processes in bimodal peat substrates, it supports the hypothesis that γ is governed by

*n*/

_{ag}*n*in such growing media. This also supports the view that for peat substrates, the lack of correlation for

*D*/

_{s}*D*may not be attributed to the hypothesized model, as indeed this confirms the validity of Eq. [17].

_{o}Figure 4 also indicates that the two-point method introduces a pronounced bias (slope significantly different from 1) in the case of mineral soils, since the γ values obtained with this method were higher than those obtained by gas diffusion chamber measurements. Meanwhile, estimates obtained with the two-point method coincided with the 1:1 curve at those γ values corresponding to peat substrates (values inside the circle on Fig. 4). The *R*^{2} of the correlation was high (0.74 on Fig. 4) and increased to 0.88 when mean values were considered (data not shown), but remained significantly biased (i.e., slope significantly different from 1). Again, this may be because of the assumption of a water desorption curve with two distinct linear zones (form saturation to around −2 kPa, and from −2 kPa to around −10 kPa) may be realistic for peat substrates but cannot be extended to the two mineral substrates (Fig. 1).

### Practical Implications

As said earlier, information about the physical properties of substrates is needed to optimize irrigation in nursery and greenhouse and to guide substrate manufacturing. Because these properties may evolve across time, a method for in situ and automatic characterization of the properties is required. Previous studies have shown that time domain reflectometry can be used to monitor water content in growing media and improve irrigation management (Murray et al., 2002). The same TDR system can be used with greenhouse crops to monitor salt accumulation in media and induce leaching during irrigation if the salt concentration is limiting plant growth. Following the pioneer work of Topp et al. (1988), Cliche (1999) indeed showed that TDR could also be used to measure salinity in peat substrates.

This study further demonstrates how time domain reflectometry can be used to gain information about the aeration process in pots and eventually enable growers to manage irrigation with as few measuring devices as possible. However, the findings of this study confirm that information on the water desorption curve and its numerical integration are still needed to obtain an unbiased estimation of γ and *D _{s}*/

*D*in growing media and that we need to refine γ estimation for better accuracy. The results indicate though that the proposed methodology can already be used to guide peat substrate manufacturing. Indeed, the information on

_{o}*K*and the whole water desorption curves is part of the routine measurements. Therefore, given the absence of bias for peat substrates and its capacity to discriminate between peat treatment, the multiple point method can be used to assess

_{s}*D*/

_{s}*D*and tortuosity without additional measuring effort. However, as a diagnostic tool for practitioners in nurseries and greenhouses, more work is still required before this procedure can be used extensively since

_{o}*K*must be measured directly in pots with an infiltrometer (Allaire et al., 1994) and ψ

_{s}*with horizontal probes (Nemati et al., 2002) to calculate γ, and these procedures are too complex for routine use by growers or practitioners. Because attempts to develop simplified procedures to automatically determine*

_{a}*K*and ψ

_{s}*at the nursery or greenhouses with a single TDR probe have had limited success (Caron et al., 2002), further efforts may seem pointless and additional work should perhaps focus on direct oxygen content or flux determination. However, for growing media, it would be still be worthwhile to continue work on aeration with the estimation of*

_{a}*D*/

_{s}*D*using the methodology proposed here. Indeed, measuring the oxygen diffusion rate has proven to be less accurate than these τ

_{o}*(1/γ) and*

_{w}*D*/

_{s}*D*estimates in predicting crop yield (Allaire et al., 1996), probably because of scale issues. Also, Cook and Knight (2003) suggested that for progress to be made on aeration, a suite of parameters (O

_{o}_{2}fluxes, air content,

*D*) needs to be measured. Finally, work on the integration of

_{s}*D*/

_{s}*D*estimates measured with a capacitive probe integrated in the irrigation procedure directly in greenhouses has shown promising results (Caron et al., 2001). Further work will therefore be performed in the future to validate the use of this approach in different growing media with a wide range of air contents, in combination with other technologies, as a simplified approach for practitioners to use directly with greenhouse and nursery potted plans.

_{o}## CONCLUSIONS

A rapid method for the estimation of gas diffusivity in situ in peat substrates at the factory, at the nursery, or at the greenhouse and based on water storage and flow measurements is presented. The method is shown to provide unbiased estimates of gas diffusivity (*R*^{2} = 0.49) and of pore effectiveness coefficient (*R*^{2} = 0.80) that are comparable with the results obtained with direct gas diffusion chamber measurements. A simpler method, requiring the measurement of only two points of the water desorption curve, was also proposed. It was found to be biased but was significantly correlated for gas diffusivity (*R*^{2} = 0.33) and pore effectiveness (*R*^{2} = 0.74) with diffusion chamber measurement estimates.

## Acknowledgments

The authors acknowledge the financial contribution of Les Entreprises Premier CDN ltée, Les Composts du Québec, La Ferme Gaétan Hamel, Fafard et Frères ltée, the Institut Québécois du Développement de l'Horticulture Ornementale, and La Pépinière Abbotsford. The financial contribution of the Quebec Ministry of Education is also recognized. We also thank Dr. J.P. Emond and F. Mercier of the Département des Sols et de Génie Agroalimentaire de l'Université Laval, N. De Rouin for their contribution, as well as G. Kluitenberg and two anonymous reviewers for their relevant comments. Finally, the special contribution of Dr. G. Clarke Topp is acknowledged. Over the past years, Dr. Topp has participated in thesis and evaluation committee work that has led, directly or indirectly, to some of the work presented here. He became involved in our work at the university first for his scientific knowledge and secondly, for his ability to communicate in French. His work style as well as the soundness and relevance of his contributions earned him great respect among his colleagues. He is and will remain known to some as “Le magnifique.”

- Received March 18, 2003.