Published online 14 April 2008
Published in Vadose Zone J 7:397-405 (2008)
DOI: 10.2136/vzj2007.0058
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Variable Pore Connectivity Factor Model for Gas Diffusivity in Unsaturated, Aggregated Soil
Augustus C. Resurrecciona,*,
Per Moldrupb,
Ken Kawamotoa,
Seiko Yoshikawac,
Dennis E. Rolstond and
Toshiko Komatsua
a Graduate School of Science and Engineering, Saitama Univ., 225 Shimo-okubo, Sakura-ku, Saitama 338-8570, Japan
b Environmental Engineering Section, Dep. of Biotechnology, Chemistry and Environmental Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
c Research Team for Conservation of Agricultural Watershed, National Agricultural Research Center for Western Region, Ikano 2575, Zentsuji, Kagawa 765–0053, Japan
d Dep. of Land, Air, and Water Resources, Univ. of California, Davis, CA 95616. A.C. Resurreccion, current address: Dep. of Engineering Sciences, Univ. of the Philippines-Diliman, Quezon City, 1101 Philippines
* Corresponding author (acresurrecci{at}up.edu.ph).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 27 March 2007.
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ABSTRACT
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The soil gas diffusion coefficient (Dp) and its variations with soil air content (
) and soil water matric potential (
) control vadose zone transport and emissions of volatile organic chemicals and greenhouse gases. This study revisits the 1904 Buckingham power-law model where Dp is proportional to X, with X characterizing the tortuosity and connectivity of air-filled pore space. One hundred years later, most models linking Dp() to soil water retention and pore size distribution still assume that the pore connectivity factor, X, is a constant for a given soil. We show that X varies strongly with both and matric potential [given as pF = log(–, cm H2O)] for individual soils ranging from undisturbed sand to aggregated volcanic ash soils (Andisols). For Andisols with bimodal pore size distribution, the X–pF function appears symmetrical. The minimum X value is typically around 2 and was observed close to of –1000 cm H2O (pF 3) when interaggregate voids are drained. To link Dp with bimodal pore size distribution, we coupled a two-region van Genuchten soil water retention model with the Buckingham Dp() model, assuming X to vary symmetrically around a given pF. The coupled model well described Dp as a function of both and for both repacked and undisturbed Andisols and for other soil types. By merely using average values of the three constants in the proposed symmetrical X–pF expression, predictions of Dp were better than with traditional models.
Abbreviations: SWC, soil water characteristic
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INTRODUCTION
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TO UNDERSTAND AND model the transport and fate of gaseous-phase contaminants in soil and the exchange of greenhouse gases from the soil to the atmosphere, accurate description of the soil gas diffusion coefficient (Dp) as a function of soil moisture status is needed (Smith et al., 2003). For example, Dp is a key parameter in the migration of volatile organic chemicals from contaminated soil sites (Jury et al., 1990; Petersen et al., 1996), in CH4 oxidation in forest and agricultural soils (Kruse et al., 1996; Ball et al., 1997), and in sanitary landfill soil covers (De Visscher and Van Cleemput, 2003). A universal description of soil gas diffusivity (Dp/Do, where Do is the gas diffusion coefficient in free air) and its dependency on soil moisture conditions and soil type has been a main research objective in soil gas physics since the ground-breaking work of Buckingham (1904).
Buckingham (1904) pioneered the research on soil gas diffusion, and suggested that the gas diffusion coefficient is related to the air-filled pore space (soil air content, ) in the form of a power function, X, where X is a connectivity factor for air-filled pore space. If X = 1, air-filled pore space will be in the form of parallel, straight pores (Gradwell, 1961), corresponding to maximum pore connectivity and minimum tortuosity of the air-filled pore space. Thus, X is proportional to the tortuosity (see Moldrup et al. [2001] for detailed analyses) and inversely related to the connectivity of the air-filled pore space. Buckingham (1904) found X 
2 based on measurements of Dp on sand, loam, and clay soils, and noted that soil texture, soil structure, and soil moisture status will probably influence the value of X. Currie (1960b), in his study of gas diffusion in dry granular porous media, reintroduced the pore connectivity factor, X, as a particle shape factor. In his subsequent study on gas diffusion in wet granular porous media, Currie (1961) suggested a greater significance for X as a measure of the complexity of the air-filled pore space due to the blocking effect of connected water films within the pores.
Buckingham (1907) introduced the concept of soil water matric potential (, in cm H2O) as the energy status of soil water in the vadose zone. Since can vary by several orders of magnitude, Schofield (1935) later used a logarithmic scale to redefine soil water matric potential as pF = log(–). The soil water matric potential ( or pF) provides a measure of soil moisture status of unsaturated soil and is directly linked to soil water content (
) and, consequently, through the soil water characteristic (SWC) curve and SWC models (e.g., Campbell, 1974; van Genuchten, 1980).
To describe the soil gas diffusivity of a given soil, Moldrup et al. (1999, 2000) suggested a constant but SWC-dependent X value, based on the Campbell (1974) pore size distribution index, b. Their connectivity factor, X = 2 + 3/b, is analogous to the Burdine (1953)–Campbell (1974) capillary tube tortuosity model for describing unsaturated hydraulic conductivity. Moldrup et al. (2004) modified the exponent in terms of air-filled porosity at = –100 cm H2O (denoted macroporosity, 100) and soil total porosity. These SWC-based Dp()/Do models, however, were developed based on undisturbed soils assuming unimodal pore size distributions.
These SWC-based Dp/Do models performed much better than the classical soil-type-independent models (e.g., Penman, 1940; Millington and Quirk, 1961) in predicting Dp()/Do of undisturbed natural field soils with different soil textures and across a wide range of soil total porosities (Moldrup et al., 2000, 2003). For volcanic ash soils exhibiting bimodal pore size distributions, however, an underestimation of Dp in the soil water matric potential range between = –100 and –15,000 cm H2O (Moldrup et al., 2003) and a large overestimation of Dp under air- and oven-dry conditions (Resurreccion et al., 2007a,b) were observed.
In all of the above-mentioned power-law Dp/Do models, the pore connectivity factor, X, was assumed to be constant for a given soil across the total range of soil water matric potential from wet to dry conditions. For wet granular porous materials having a dual-porosity structure, Currie (1961) observed a variation of X with soil water content, where X decreased with a decrease in soil water content to a minimum value and increased again when the pores inside the soil crumbs (soil aggregates) started to drain. More recently, Moldrup et al. (2005) showed, for 44 differently textured undisturbed soils, that X is expected to vary from 2 for drier soil to 2.5 or more for wetter soil, and suggested the possibility of linking X with soil water matric potential to better predict the soil gas diffusivity behavior.
Several studies suggested a direct link of soil gas diffusivity to pore size distribution through a SWC function. Moldrup et al. (2005) directly linked the power-law Dp() model by Moldrup et al. (2004) with pF, using the unimodal van Genuchten (1980) SWC model. This yielded a closed-form Dp(pF) function to predict SWC effects on Dp(), but still assumed a constant X for a given soil. Freijer (1994) applied the tortuous jointed-tube model by Ball (1981) to describe soil gas diffusivity variations with , and also suggested possible links between Dp() and the parameters in the unimodal van Genuchten (1980) SWC function. To our knowledge, possible variations of X with soil water matric potential and the effect of bimodal pore size distribution on soil gas diffusivity have not yet been considered in a descriptive Dp model.
The objectives of this study were (i) to evaluate the dependency of the connectivity of air-filled pore space (as denoted by X) on soil water matric potential for different soil types and, in particular, for aggregated volcanic ash soils, (ii) to describe the Dp()/Do behavior of aggregated unsaturated volcanic ash soils by coupling a bimodal SWC model with the classical Buckingham (1904) Dp/Do model, allowing X to vary with soil water matric potential, and (iii) to use the coupled gas diffusivity–water retention model to explain the contribution of inter- and intraaggregate pore space to soil gas diffusion in unsaturated, aggregated soils.
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Theory
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The Pore Connectivity Factor
The relation between the soil gas diffusivity (Dp/Do) and the soil air content () as suggested by Buckingham (1904) is
 | [1] |
where X is the pore connectivity factor that can be calculated from the measured Dp()/Do by (Currie, 1960b)
 | [2] |
Equation [1] is a simplified analogy to the expression for thermal conductivity of heterogeneous mixtures by Bruggeman (1935). Traditionally, X has been assumed to be constant for a given soil (Moldrup et al., 2001). As shown by Currie (1961) and Moldrup et al. (2005), however, the Buckingham–Currie pore connectivity factor X varies with the soil moisture status.
In this study, we suggest that X changes not only with , as shown by Currie (1961) for wet granular materials with a dual porosity system, but also with soil water matric potential (in terms of pF). We assume that the X–pF relation can be described by a four-parameter symmetrical function:
 | [3] |
where A1, A2, B, and pF* are curve-fitting constants. The reference soil water matric potential, pF*, divides the inter- and intraaggregate pore space regions at the point where the pore connectivity factor assumes a minimum value of X = B, thereby assuming that maximum air-filled pore connectivity occurs just before the intraaggregate pores start to drain, creating a minimum water blocking effect within the air-filled (interaggregate) pore space. During subsequent drainage, the interaggregate pore space will still have a minimal water blocking effect but the intraaggregate pore space will start to drain, creating inactive air-filled pore space within the aggregates, causing X to increase again. It should be noted that X reflects the bulk pore connectivity of the air-filled (both inter- and intraaggregate) pore space. For Andisols, detailed soil water retention data suggested that pF* was close to 3 (Kawamoto and Aung, 2004). For sand (structureless), we may assume pF* = 6.9, which is the maximum theoretical value of pF (Groenevelt and Grant, 2004), to yield a monotonically decreasing X(pF) function.
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Coupling Gas Diffusivity and Bimodal Soil Water Characteristic Models
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The bimodal van Genuchten SWC model (Durner, 1994) describes the soil water content () as a function of soil water matric potential () and can be interpreted as the cumulative contribution to soil water content in the inter- and intraaggregate pore space regions. The bimodal SWC model is
 | [4] |
where s is the soil water content at saturation (m3 m–3), r is the irreducible soil water content (m3 m–3), is the soil water matric potential (cm H2O), w1 and w2 are the weighing factors (adding up to unity), 
1 and 2 are the scale factors (cm–1), and n1, n2, m1 (= 1 – 1/n1), and m2 (= 1 – 1/n2) are the shape factors. The scale factors, shape factors, weights, and residual soil water content are curve-fitting parameters obtained from the soil water retention data by using the SOLVER tool in Microsoft Excel (Wraith and Or, 1998). In this study, s was assumed equal to the soil total porosity (
), which is the sum of and :
 | [5] |
A closed-form expression for soil gas diffusivity as a function of pF is derived by combining Eq. [1], [4], and [5], yielding
 | [6] |
where X can be assumed either to be a constant or to vary with pF (e.g., following Eq. [3]). Finally, to use the coupled model for calculating Dp()/Do with a symmetric X(pF) function, Dp()/Do is calculated from the Buckingham (1904) Dp()/Do model (Eq. [1]), with X varying with pF according to Eq. [3]. This yields
 | [7] |
When using Eq. [7], the soil water matric potential (pF) that corresponds to a given (= – ) value is calculated from the bimodal SWC model (Eq. [4]).
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Materials and Methods
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Soils and Data
The soil water retention and Dp/Do data used in this study were taken from the literature (Osozawa, 1998; Resurreccion et al., 2007a,b). In addition, measurements on a repacked volcanic ash soil (Andisol) and on Toyoura fine sand were conducted during this study. All measurements of soil water retention and Dp were done using 100-cm3 core samples at a wide range of soil water matric potential values from near water saturation to air-dry conditions. Measurements in this study and by Resurreccion et al. (2007a,b) were conducted on 100-cm3 cores with 5.6-cm diameter and 4.06-cm height, while Osozawa (1998) used 100-cm3 cores with 5.04-cm diameter and 5.0-cm height. All soils were taken from various locations in Japan and are in this study referred to according to the sampling location (name of the local area) and in some cases soil sampling depth.
We used data for nine soils from Osozawa (1998), representing four different soil types: a Yellow soil (Toyohashi), Dune sand (Kashima), Gray-Lowland soils (Alakawa or Saitama paddy field), and Andisols (Tsukuba or Tsumagoi). Soil conditions were either repacked (two soils: the Kashima Dune sand and Tsukuba Andisol), undisturbed (three soils: two Saitama Gray-Lowland soils and the Tsumagoi Andisol), or from 7-yr old soil lysimeters (four soils: the Toyohashi Yellow soil, Kashima Dune sand, Alakawa Gray-Lowland soil, and Tsukuba Andisol). The repacked soils were passed through a 2-mm sieve before packing into 100-cm3 soil cores, while soils taken from either agricultural fields (referred to as undisturbed soils) or soil lysimeters were collected by inserting a 100-cm3 soil core into the soil. The undisturbed Saitama paddy field Gray-Lowland soils were either uncompacted or uniaxially compacted at 100 kPa. The soil water retention and Dp/Do data represent mean values of triplicate sample measurements. A pF value of 6 was adopted for air-dry conditions following Poulsen et al. (2006).
We also used the data of Resurreccion et al. (2007a,b) representing four volcanic ash soils with different soil organic matter contents. Only data sets for 19 undisturbed Andisol samples (out of a total of 48) that included Dp measurements under air-dry conditions were used in this study. The data represent six soil samples (referred to as Nishi-Tokyo) collected at 5- to 10-cm depth along a field transect in a pasture field in Nishi-Tokyo, Japan (Resurreccion et al., 2007a) and 13 soil samples taken from a forest site in Fukushima, Japan (Resurreccion et al., 2007b) at depths of 0 to 5 cm (referred to as Fukushima 0–5, five samples), 15 to 20 cm (Fukushima 15–20, four samples), and 55 to 60 cm (Fukushima 55–60, four samples). An overview of the data sets showing the average bulk density, total porosity, soil texture, and soil organic matter is given in Table 1
. Measurements of Dp on these 100-cm3 soil samples were done at pF 1.0, 1.8, 2.0, 3.0, 4.1, and 6 (air dry). Detailed descriptions of the sampling procedure and soil physical characteristics are given in Resurreccion et al. (2007a,b).
In the present study, disturbed soil was collected from Nishi-Tokyo (the same sampling location where the undisturbed Nishi-Tokyo samples were taken), sieved (2 mm), and repacked into 100-cm3 cores at 0.73 g cm–3 bulk density close to the field bulk density. The soil samples were saturated with water and drained to pF 1, 1.5, 1.8, 2, 2.3, 3, 4.1, and 6. Measurements of soil water retention and Dp/Do were done in triplicate and the mean values were used in this study. We also measured gas diffusivity on repacked Toyoura fine sand. Samples were prepared differently to obtain data that represented a wide range of (and thus ) values. Air-dried sand was mixed with water inside a transparent plastic bag to achieve volumetric water contents between 0.01 and 0.3 m3 m–3 when packed into 100-cm3 soil cores at 1.58 g cm–3 bulk density (highly compacted). The sand–water mixture was sealed, kept for 3 d, and occasionally shaken to achieve a uniform distribution of water. The soil water content was checked by random sampling (three samples) from the sand–water mixture and the mean value was compared with the soil water content after the Dp measurement. The mean values of Dp/Do (duplicate) were used in the analysis. Soil water retention was measured on separate samples. The soil physical characteristics of the repacked Nishi-Tokyo Andisol and Toyoura sand are shown in Table 1.
Measurement Methods
For all data sets (from the literature and this study), the same experimental methods for soil water retention and Dp measurements were used. Soil water retention was measured using a draining curve, using either a hanging water column for pF 
2 (i.e., 
–100 cm H2O) or a pressure plate extractor (Soilmoisture Equipment Corp., Santa Barbara, CA) for pF > 2 (i.e., < –100 cm H2O). Resurreccion et al. (2007a,b), however, used only the pressure plate extractor across the entire pF interval. Except for the Toyoura sand, the soil samples were first saturated with water and then drained subsequently to different pF conditions where Dp was measured at each drainage step. Before measurements of Dp, soil samples were weighed to determine the soil water content at each pF. For the air-dry condition (pF 6), samples were placed inside a convective air-flow oven set at 20°C for 5 to 7 d.
The soil gas diffusion coefficients (Dp) were measured by the method of Currie (1960a) as recommended by Rolston and Moldrup (2002). The apparatus uses a diffusion chamber with O2 as the experimental gas at 20°C. The diffusion chamber was flushed with 100% N2 gas while the upper end of the soil core was exposed to the atmosphere. The O2 inside the diffusion chamber was measured by an O2 electrode connected to a CR10X datalogger (Campbell Scientific, Logan, UT). Schjønning (1985) and Moldrup et al. (2000) have shown for the same experimental setup that the O2 consumption rate can be considered negligible for the short measurement time (minutes to a few hours, depending on the pF condition) needed to measure Dp. Mixing of air within the small diffusion chamber was assumed to occur instantly. The calculation of Dp was done according to Rolston and Moldrup (2002).
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Results and Discussion
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Figure 1
shows the soil gas diffusivities (Dp/Do) for the nine soils from Osozawa (1998) representing four soil types (Yellow soil, Dune sand, Gray-Lowland soil, and Andisol) under repacked, lysimeter, or undisturbed soil conditions. The Dp/Do for each soil increased with , and each soil exhibited a unique Dp()/Do behavior (Fig. 1a, 1d, and 1g) due to differences in soil type and structure.
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FIG. 1. Plots of the (a, d, and g) soil gas diffusivity (Dp/Do) against soil air-content (), and the Buckingham–Currie pore connectivity factor (X) calculated using Eq. [2] (b, e, and h) against and (c, f, and i) against pF = log(–, matric potential in cm H2O) for Japanese soils with different soil texture and structure (100 kPa denotes 100-kPa uniaxial compaction). Fitted X(pF) functions, Eq. [3], for each soil are also shown in (c), (f), and (i). Data from Osozawa (1998).
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Except for the repacked Dune sand, the Buckingham Dp()/Do model (Eq. [1]) with a constant X failed to describe the Dp()/Do data since X (calculated using Eq. [2]) changed with . This implies a strong dependency of X on soil moisture conditions (Fig. 1b, 1e, and 1h), as also observed by Currie (1961) for repacked soil aggregates or crumbs. When X was plotted against pF, each soil exhibited a clear and distinct X–pF relation (Fig. 1c, 1f, and 1i) that represents a fingerprint of soil structure. Each soil exhibited a unique fingerprint, with the highly structured Gray-Lowland soils showing a dramatic decrease in X around pF 2.5 to 3, probably due to the smaller air-filled pores drained at pF 2.5 to 3 suddenly interconnecting with the previously drained cracks and macropores (e.g., from decayed plant root burrows in the paddy field soil), creating highly connected air-filled pathways through the soils.
The X(pF) functions that best describe the variation of X with pF for Dune sands and Yellow soil changed from a constant (X = 1.71) for the repacked Kashima Dune sand to a continuously decreasing X(pF) function (Eq. [3] with pF* = 6.9) for the lysimeter Kashima Dune sand where some soil structure had been created during the 7 yr from the packing of the outdoor lysimeters to soil sampling (Fig. 1c). In the case of the Gray-Lowland soils (Fig. 1f), the symmetrical X(pF) function (Eq. [3]) only provided a good fit to the Alakawa lysimeter soil and the undisturbed, uncompacted Saitama paddy field soil. The measured X–pF data for the paddy field soil became asymmetrical with uniaxial compaction. Thus, a mathematically more flexible and asymmetrical X(pF) function is needed to also take into account compaction effects on highly structured soils. For the well-aggregated Andisols (Fig. 1i), Eq. [3] accurately fitted the X–pF data for the Tsukuba and Tsumagoi Andisols. The pore connectivity factor X decreased with pF to a minimum value at around pF 3 and increased again to a large X value at the air-dry condition (pF 6).
Figure 2
illustrates the concept of linking the Buckingham Dp/Do model, Eq. [1], with pore size distribution described by the bimodal SWC model, Eq. [4], for different soil types. The measured SWC curves (closed symbols) and fits by the bimodal SWC model are shown in Fig. 2a and 2c for six different soils. The bimodal SWC model accurately represented the SWC data of both repacked and undisturbed Andisols across soil moisture conditions, while a single-region SWC model led to fitting problems at the intermediate soil moisture conditions as a result of the formation of secondary pore systems within the aggregates (Durner, 1994). The SWC curve of the Toyoura sand was adequately described, however, by a unimodal SWC model (w1 = 1, w2 = 0; see Table 1) and zero residual water content (r = 0), while requiring a very high shape factor (n = 7.17). The remaining five soils required a bimodal SWC model to obtain a good description of the soil water retention data.
The bimodal Dp/Do models, Eq. [6] and [7], together with the symmetrical X–pF function (Eq. [3]), accurately described the variations of measured Dp/Do with pF (Fig. 2a and 2c) and the Dp()/Do behavior (Fig. 2b and 2d). A comparison of Dp/Do behavior of the different soils, having completely different pore size distributions (SWC curves), implies a large effect of soil type and bimodal pore size distribution on the soil gas diffusion coefficient. Interestingly, only a small difference between the repacked and undisturbed Nishi-Tokyo Andisol was observed, both with respect to pore size distribution and soil gas diffusivity behavior (Fig. 2c and 2d), suggesting a well-developed aggregate soil structure in both types of samples (Moldrup et al., 2003).
We note that merely using constant X (=1.71) for the repacked Toyoura sand, adopted from the description of the repacked Kashima Dune sand in Fig. 1c, together with a unimodal SWC model adequately predicted the Dp() and Dp(pF) for this repacked sand with a narrow particle size distribution (Fig. 2c and 2d). A slight scatter in the measured Dp/Do data was observed, as each measurement point represents an individually packed sample with slight differences in total porosities and, hence, in the water blockage effect between particles at a given air-filled porosity. A minor improvement in Dp/Do model accuracy was obtained by assuming a symmetric X(pF) function with pF* = 6.9 for this highly compacted Toyoura sand (not shown), probably due to additional water blockage effects at low air-filled porosity at high compaction (Shimamura, 1992).
Since the minimum value of the Buckingham–Currie pore connectivity factor (X) occurred close to pF 3 for Andisols in both Fig. 1 and 2, this phenomenon was investigated further. In Fig. 3a
, gas diffusivity data from 58 different soils (14 soils used in this study and 44 additional soils from Osozawa [1998]) were considered to examine the variations of X with soil type at pF 3. The X values at pF 3 were, in general, close to the value of X 2 suggested by Buckingham (1904), especially for the well-aggregated Andisols. No increasing trend of X values with increasing at pF 3 was observed for the Andisols, implying that the air-filled pore connectivity between aggregates was not markedly affected by at pF 3. A soil moisture condition close to pF 3 results in a maximum continuity (connectivity) of air-filled pore space where X assumes a minimum value, as also observed in Fig. 1i. This is probably because voids between aggregates are almost fully drained (only irreducible water left) at a soil water matric potential around –1000 cm H2O (pF 3), eliminating interconnected water films between water-filled aggregates. A transitional drainage sequence from inter- to intraaggregate pore space was also suggested and supported by data from Currie (1961).
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FIG. 3. (a) Plot of the pore connectivity factor (X) against soil water content, , at pF 3 for Japanese soils. Filled symbols represent Yellow soils (blue), Gray-Lowland soils (red), and Andisols (black). (b) The symmetric X(pF) function, Eq. [3], fitted to the X–pF data of 19 undisturbed Andisol samples (filled circles, data from Resurreccion et al., 2007a,b) is shown. Also shown are the X–pF data from Moldrup et al. (2005) (open circles) and for an undisturbed Tsumagoi Andisol (open triangles, data from Osozawa, 1998). A symmetric X–pF function with A1 = 0.15, A2 = 2, B = 2, and pF* = 3 is also plotted in (b).
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The X values of the 19 individual Nishi-Tokyo and Fukushima Andisol samples at each pF measurement agreed well with the data from Moldrup et al. (2005) for 44 differently textured intact Andisol samples (Fig. 3b). Similar to the observations for the undisturbed Tsumagoi Andisol in Fig. 3b (as also shown in Fig. 1i), the X values increased as pF decreased at pF < 3. This is because tortuosity increased (reducing air-filled pore connectivity) due to isolated (entrapped) air-filled pores, particularly at very high soil water content (e.g., at pF 1). At pF > 3, X increased to a high value under dry conditions due to the additional air-filled space inside aggregates being remote and separated from the main interaggregate pathways of diffusion. These data on undisturbed Andisols further support the hypothesis that X has a minimum value at a soil water matric potential close to = –1000 cm H2O (pF 3, corresponding to an equivalent pore diameter of around 3 µm). Fitting the suggested symmetric X(pF) function, Eq. [3], we obtained A1 = 0.185, A2 = 1.78, B = 2.11, and pF* = 3.13 to describe the relationship between X and pF for these undisturbed aggregated Andisols (Fig. 3b). As a simple, average model for all the different Andisol data sets in Fig. 1 and 2, we will assume B = 2 (suggested by Buckingham, 1904) at pF* = 3, A1 = 0.15, and A2 = 2 to be used in Eq. [3] for predicting Dp/Do in unsaturated Andisols.
The proposed bimodal Dp/Do models are compared with some of the commonly used Dp/Do models in Fig. 4
, using data for the three undisturbed Andisol layers from Fukushima (data from Resurreccion et al., 2007b). Equation [4] fitted well the soil water retention data (Fig. 4a, 4d, and 4g). The fitted soil water retention parameters are given in Table 1. In agreement with the observations made in Fig. 3, the soil water retention point where the separation between inter- and intraaggregate pore regions takes place was estimated to be near pF 3.
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FIG. 4. (a, d, and g) The two-region Durner (1994) soil–water retention model (solid lines) fitted to the soil water retention data of three undisturbed Japanese Andisols. The contributions of inter-and intra-aggregate pore space regions to soil water retention are shown as dashed lines. The average gas diffusivity (Dp/Do) and Dp/Do models (Eq. [6] and [7]) using the symmetrical X(pF) function (Eq. [3] with A1 = 0.185, A2 = 1.78, B = 2.11, and pF* = 3.13) are plotted against (b, e, and h) pF and (c, f, and i) soil air content, . Also shown are the Dp/Do predictions using X = 2, X = 2 + 0.15 |pF – 3|2, and the commonly used Dp()/Do models of Penman (1940) and Millington and Quirk (1961).
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With the bimodal soil water retention model (Eq. [4]) but using a constant X value (X = 2), the predictions of the bimodal Dp(pF)/Do model overestimated the measured values, especially at pF > 3 (Fig. 4b, 4e, and 4h). By using the fitted parameter values of the X–pF function (Eq. [3] with A1 = 0.185, A2 = 1.78, B = 2.11, and pF* = 3.13; cf. Fig. 3b), the coupled bimodal Dp(pF)/Do and Dp()/Do models (Eq. [6] and [7]) accurately captured the Dp/Do data throughout the entire range of measured soil water conditions. A good description of the measured Dp/Do data was obtained if the average Andisol parameter values based on setting B = 2 at pF* = 3 were used (A1 = 0.15, A2 = 2). The coupled Dp(pF)/Do model showed a strong tendency of bimodality and mirrored the dual S-shaped soil water retention curve. In comparison, the classical and widely used Dp()/Do models of Penman (1940) and Millington and Quirk (1961) failed to describe the gas diffusivity behavior (Fig. 4c, 4f, and 4i).
The Dp()/Do curves for Andisols, which from the bimodal Dp/Do models can now be partitioned into components of inter- and intraaggregate pore volumes, are similar in shape to the Dp()/Do curves for repacked soil crumbs measured in the classical study by Currie (1961). The Dp()/Do curves by Currie (1961), however, exhibited a more distinct change in gas diffusivity behavior between inter- and intraaggregate pore space, probably due to a more distinct bimodal pore size distribution of these pure aggregate size fractions.
Figure 5
shows a model sensitivity analysis with respect to the effects of soil water retention parameters (Fig. 5a) on predicted soil gas diffusivity in aggregated soils. A slight change in the shape factors for the inter- and intraaggregate pore size distributions as well as in the fraction of intraaggregate pores markedly affect both Dp() and Dp(pF) behavior (Fig. 5b and 5c). Likewise, varying the parameters in the symmetrical X–pF expression, Eq. [3], showed a marked effect on the behavior of Dp() (Fig. 5d). Interestingly, Fig. 5 implies that the combined effect of bimodal pore size distribution and associated effects on pore connectivity variations controls the changes in Dp/Do during varying soil moisture conditions. The combined effects of the dramatic change in pore connectivity from the interaggregate to intraaggregate regions and the complicated dual-porosity pore size distribution to some extent seem to counteract each other, creating an apparently simple and almost linear increase in Dp/Do with increasing (Fig. 5d). In contrast, a constant X value (e.g., X = 2 as suggested by Buckingham) will give the nonlinear, power-law curve (Fig. 5d) assumed by most of the traditionally used, predictive gas diffusivity models. The analyses in Fig. 5 show that these traditionally used models are not valid for aggregated soils across soil moisture conditions and pF values.
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FIG. 5. (a) Soil water retention curves at different weight distributions and shape factors, and (b and c) the effect of weight distribution of the inter- and intraaggregate porosity (w1 and w2) and shape factors (n1 and n2) on gas diffusivity, Dp/Do. When not varied, the shape factors are n1 = 1.7 and n2 = 1.3, and weights w1 and w2 are equal to 0.5. A symmetrical X–pF function (Eq. [3] with A1 = 0.185, A2 = 1.78, B = 2.11, and pF* = 3.13) was used in (b) and (c). (d) Effect of parameters of the symmetrical X–pF function on Dp/Do at the given soil water retention parameters. For all plots, saturated water content, s, is 0.75 m3 m–3 and scaling factors 1 and 2 are 0.075 and 0.00005 cm–1, respectively.
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Large differences in Dp/Do can be seen at the same pF values (Fig. 5c). For example, a given Dp/Do value necessary for adequate soil aeration (e.g., Dp/Do = 0.05) will occur at widely different pF values depending on the combination of the soil water retention parameters. This supports the hypothesis that both soil aggregate size distribution and soil compaction (which will mostly reduce interaggregate pore space) will have marked effects on Dp and thus on soil aeration and plant welfare, as also discussed by Grable and Siemer (1968).
In perspective, this study suggests the need for developing predictive bimodal Dp/Do models that take into consideration separate contributions from the inter- and intraaggregate pore space, preferably based on easily obtainable input parameters. This study and the dual probability-law model study by Poulsen et al. (2006) are significant steps toward this model development. For example, the point of minimum X on the soil structure fingerprint plots (Fig. 1c, 1f, and 1i) can be used to more accurately identify the border between inter- and intraaggregate regions in aggregated soil with respect to gas transport behavior. When sufficient data become available, an improved and more conceptual description of the pore connectivity factor and its variation with soil water matric potential for different soil types and conditions may be the key to understanding the effects of soil structure on gas diffusivity in the soil vadose zone.
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Conclusions
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The classical gas diffusion study of Buckingham (1904) was revisited to link the Buckingham air-filled pore space connectivity with soil moisture conditions to describe the behavior of soil gas diffusivity. The magnitude and variation of X was found to be highly dependent on soil water matric potential (expressed as pF), with each soil type and condition (e.g., compaction or repacking) exhibiting a unique X–pF relationship (a soil structure fingerprint).
For well-aggregated volcanic ash soils (Andisols), the proposed X(pF) function, being symmetrical around pF 3, accurately described the relation between X and pF. By linking X with pF and coupling the Buckingham gas diffusivity model with a two-region soil water retention model to describe bimodal pore size distributions, the new descriptive, bimodal Dp/Do model satisfactorily explained the relative gas diffusivity behavior for aggregated soils and the contributions from the inter- and intraaggregate pore space regions.
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ACKNOWLEDGMENTS
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This study was made possible by the Grant-In-Aid for Scientific Research no. 18360224 from the Japan Society for the Promotion of Science (JSPS) and by a grant from the Innovative Research Organization, Saitama University. This study was in part supported by the projects Gas Diffusivity in Intact Unsaturated Soil ("GADIUS") and Soil Infrastructure, Interfaces, and Translocation Processes in Inner Space ("Soil-it-is") from the Danish Research Council for Technology and Production Sciences, and by Grant no. P42 ES04699 from the National Institute of Environmental Health Sciences (NIEHS), NIH. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIEHS, NIH.
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REFERENCES
|
|---|
- Ball, B.C. 1981. Modeling of soil pores as tubes using gas permeabilities, gas diffusivities and water release. J. Soil Sci. 32:465–481.[CrossRef]
- Ball, B.C., K.E. Dobbie, J.P. Parker, and K.A. Smith. 1997. The influence of gas transport and porosity on methane oxidation in soils. J. Geophys. Res. 102:23301–23308.[CrossRef]
- Bruggeman, D.A.G. 1935. The prediction of the thermal conductivity of heterogeneous mixtures. Ann. Phys. 24:636–664.
- Buckingham, E. 1904. Contributions to our knowledge of the aeration of soils. USDA Bur. Soil Bull. 25. U.S. Gov. Print. Office, Washington, DC.
- Buckingham, E. 1907. Studies on the movement of soil moisture. USDA Bur. Soil Bull. 38. U.S. Gov. Print. Office, Washington, DC.
- Burdine, N.T. 1953. Relative permeability calculations from pore-size distribution data. Trans. AIME 198:71–78.
- Campbell, G.S. 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci. 117:311–314.
- Currie, J.A. 1960a. Gaseous diffusion in porous media: Part 1. A nonsteady state method. Br. J. Appl. Phys. 11:314–317.[CrossRef]
- Currie, J.A. 1960b. Gaseous diffusion in porous media: Part 2. Dry granular materials. Br. J. Appl. Phys. 11:318–324.[CrossRef]
- Currie, J.A. 1961. Gaseous diffusion in porous media: Part 3. Wet granular materials. Br. J. Appl. Phys. 12:275–281.[Medline]
- De Visscher, A., and O. Van Cleemput. 2003. Simulation model for gas diffusion and methane oxidation in landfill cover soils. Waste Manage. 23:581–591.[CrossRef]
- Durner, W. 1994. Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resour. Res. 30:211–223.[CrossRef]
- Freijer, J.I. 1994. Calibration of jointed tube model for the gas diffusion coefficient in soils. Soil Sci. Soc. Am. J. 58:1067–1076.[Abstract/Free Full Text]
- Grable, A.R., and E.G. Siemer. 1968. Effects of bulk density, aggregate size, and soil-water suction on oxygen diffusion, redox potentials, and elongation of corn roots. Soil Sci. Soc. Am. Proc. 32:180–187.
- Gradwell, M.W. 1961. A laboratory study of the diffusion of oxygen through pasture topsoils. N.Z. J. Agric. Res. 4:250–270.
- Groenevelt, P.H., and C.D. Grant. 2004. A new model for the soil-water retention curve that solves the problem of residual water contents. Eur. J. Soil Sci. 55:479–485.[CrossRef]
- Jury, W.A., D. Russo, G. Streile, and H. El Abd. 1990. Evaluation of volatilization by organic chemicals residing below the soil surface. Water Resour. Res. 26:13–20.[CrossRef]
- Kawamoto, K., and B. Aung. 2004. Experimental study on soil water repellency of volcanic ash soils: Effects of organic matter content and initial water content. (In Japanese with English summary.) Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 230:75–83.
- Kruse, C.W., P. Moldrup, and N. Iversen. 1996. Modeling diffusion and reaction in soils: II. Atmospheric methane diffusion and consumption in forest soil. Soil Sci. 161:355–365.[CrossRef]
- Millington, R.J., and J.M. Quirk. 1961. Permeability of porous solids. Trans. Faraday Soc. 57:1200–1207.[CrossRef]
- Moldrup, P., T. Olesen, T. Komatsu, P. Schjønning, and D.E. Rolston. 2001. Tortuosity, diffusivity, and permeability in the soil liquid and gaseous phases. Soil Sci. Soc. Am. J. 65:613–623.[Abstract/Free Full Text]
- Moldrup, P., T. Olesen, P. Schjønning, T. Yamaguchi, and D.E. Rolston. 2000. Predicting the gas diffusion coefficient in undisturbed soil from soil water characteristics. Soil Sci. Soc. Am. J. 64:94–100.[Abstract/Free Full Text]
- Moldrup, P., T. Olesen, T. Yamaguchi, P. Schjønning, and D.E. Rolston. 1999. Modeling diffusion and reaction in soils: IX. The Buckingham–Burdine–Campbell equation for gas diffusivity in undisturbed soil. Soil Sci. 164:542–551.[CrossRef]
- Moldrup, P., T. Olesen, S. Yoshikawa, T. Komatsu, and D.E. Rolston. 2004. Three-porosity model for predicting the gas diffusion coefficient in undisturbed soil. Soil Sci. Soc. Am. J. 68:750–759.[Abstract/Free Full Text]
- Moldrup, P., T. Olesen, S. Yoshikawa, T. Komatsu, and D.E. Rolston. 2005. Predictive-descriptive models for gas and solute diffusion coefficients in variably saturated porous media coupled to pore-size distribution: II. Gas diffusivity in undisturbed soil. Soil Sci. 170:854–866.[CrossRef]
- Moldrup, P., S. Yoshikawa, T. Olesen, T. Komatsu, and D.E. Rolston. 2003. Gas diffusivity in undisturbed volcanic ash soils: Test of soil-water-characteristic based prediction models. Soil Sci. Soc. Am. J. 67:41–51.[Abstract/Free Full Text]
- Osozawa, S. 1998. A simple method for determining the gas diffusion coefficient in soil and its application to soil diagnosis and analysis of gas movement in soil. (In Japanese with English summary.) Ph.D. diss. Natl. Inst. of Agro-Environmental Sci., Ibaraki, Japan.
- Penman, H.L. 1940. Gas and vapor movements in soil: The diffusion of vapors through porous solids. J. Agric. Sci. 30:437–462.
- Petersen, L.W., Y.H. El-Farhan, P. Moldrup, D.E. Rolston, and T. Yamaguchi. 1996. Transient diffusion, adsorption, and emission of volatile organic vapors in soils with fluctuating low water contents. J. Environ. Qual. 25:1054–1063.[Abstract/Free Full Text]
- Poulsen, T., P. Moldrup, S. Yoshikawa, and T. Komatsu. 2006. Bimodal probability law model for unified description of water retention, air and water permeability, and gas diffusivity in variably saturated soil. Vadose Zone J. 5:1119–1128.[Abstract/Free Full Text]
- Resurreccion, A.C., K. Kawamoto, T. Komatsu, P. Moldrup, N. Ozaki, and D.E. Rolston. 2007a. Gas transport parameters along field transects of a volcanic ash soil. Soil Sci. 172:3–16.[CrossRef]
- Resurreccion, A.C., K. Kawamoto, T. Komatsu, P. Moldrup, K. Sato, and D.E. Rolston. 2007b. Gas diffusivity and air permeability in a volcanic ash soil profile: Effects of organic matter and water retention. Soil Sci. 172:432–443.[CrossRef]
- Rolston, D.E., and P. Moldrup. 2002. Gas diffusivity. p. 1113–1139. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA, Madison, WI.
- Schjønning, P. 1985. A laboratory method for the determination of gas diffusion in soil. (In Danish, with English summary.) Rep. S1773. Danish Inst. of Agric. Sci., Jyndevad.
- Schofield, R.K. 1935. The pF of the water in soil. p. 37–48. In Trans. Int. Congr. Soil Sci., 3rd, Oxford, UK. July–Aug. 1935. Vol. 2.
- Shimamura, K. 1992. Gas diffusion through compacted sands. Soil Sci. 153:274–279.
- Smith, K.A., T. Ball, F. Conen, K.E. Dobbie, J. Massheder, and A. Ray. 2003. Exchange of greenhouse gases between soil and atmosphere: Interactions of soil physical factors and biological processes. Eur. J. Soil Sci. 54:779–791.[CrossRef]
- van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.[Abstract/Free Full Text]
- Wraith, J.M., and D. Or. 1998. Nonlinear parameter estimation using spreadsheet software. J. Nat. Resour. Life Sci. Educ. 27:13–19.
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ABSTRACT
INTRODUCTION
b), soil organic matter content, soil texture, total porosity (