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Soil Science Society of America Journal 64:94-100 (2000)
© 2000 Soil Science Society of America

DIVISION S-1-SOIL PHYSICS

Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

P. Moldrupa, T. Olesena, P. Schjønningb, T. Yamaguchic and D.E. Rolstond

a Environ. Engineering Lab., Dep. of Civil Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
b Dep. of Crop Physiology and Soil Sci., Danish Inst. of Agric. Sci., Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
c Dep. of Civil and Environ. Engineering, Faculty of Engineering, Hiroshima Univ., 1-4-1 Kagamiyama, Higashi-Hiroshima, 739, Japan
d Soils and Biogeochemistry, Dep. of Land, Air, and Water Resour., Univ. of California, Davis, CA 95616 USA

i5pm{at}civil.auc.dk


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Materials and methods
 Results and discussion
 Conclusions
 REFERENCES
 
The gas diffusion coefficient in soil (DP), and its dependency on soil physical characteristics, governs the diffusive transport of oxygen, greenhouse gases, fumigants, and volatile organic pollutants in agricultural, forest, and urban soils. Accurate models for predicting DP as a function of air-filled porosity ({epsilon}) in natural, undisturbed soil are needed for realistic gas transport and fate simulations. Using data from 126 undisturbed soil layers, we obtained a high correlation (r2 = 0.97) for a simple, nonlinear expression describing DP at -100 cm H2O of soil water potential (DP,100) as a function of the corresponding air-filled porosity ({epsilon}100), equal to the volume of soil pores with an equivalent pore diameter >30 µm. A new DP({epsilon}) model was developed by combining the DP,100({epsilon}100) expression with the Burdine relative hydraulic conductivity model, the latter modified to predict relative gas diffusivity in unsaturated soil. The DP,100 and Burdine terms in the DP({epsilon}) model are both related to the soil water characteristic (SWC) curve and, thus, the actual pore-size distribution within the water content range considered. The DP({epsilon}) model requires knowledge of the soil's air-filled and total porosities and a minimum of two points on the SWC curve, including a measurement at -100 cm H2O. When tested against independent gas diffusivity data for 21 differently textured and undisturbed soils, the SWC-dependent DP({epsilon}) model accurately predicted measured data and gave a reduction in root mean square error of prediction between 58 and 83% compared to the classical, soil type-independent Penman and Millington-Quirk models. To further test the new DP({epsilon}) model, gas diffusivity and SWC measurements on undisturbed soil cores from three 0.4-m soil horizons (sandy clay loam, sandy loam, and loamy sand) within the 4 to 7 m depth below an industrially polluted soil site were carried out. For these deep subsurface soils the SWC-dependent model best predicted the measured gas diffusivities.

Abbreviations: MQ, Millington and Quirk • PMQ, Penman-Millington-Quirk • RMSE, root mean square error • SWC, soil water characteristic


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Materials and methods
 Results and discussion
 Conclusions
 REFERENCES
 
THE GAS DIFFUSION COEFFICIENT IN SOIL

(DP) and its variations with soil type and soil air–filled porosity ({epsilon}) typically control soil aeration (Buckingham, 1904; Taylor, 1949), fumigant emissions (Brown and Rolston, 1980), volatilization of volatile organic chemicals from industrially polluted soils (Petersen et al., 1996), and soil uptake or emission of greenhouse gases such as methane (Kruse et al., 1996). Accurate, predictive DP({epsilon}) models representative of natural, undisturbed soils are essential to better simulate and understand these gas transport and fate processes.

Early DP({epsilon}) models depended only on the soil air–filled porosity (Buckingham, 1904; Penman, 1940; Call, 1957). The most widely used of these one-parameter models is the Penman (1940) model

(1)
where DP is the gas diffusion coefficient in soil (cm3 soil air cm-1 soil sec-1), D0 is the gas diffusion coefficient in free air (cm2 air sec-1), and {epsilon} is the soil air–filled porosity (cm3 soil air cm-3 soil).

The next generation of DP models also included soil-type effects in the form of the soil total porosity, {Phi} (m3 m-3) (Millington and Quirk, 1960, 1961; Lai et al., 1976). The most widely used two-parameter model is that of Millington and Quirk (1961):

(2)

Comparing gas diffusivity models with measured data for a number of differently textured sieved and repacked soils, Jin and Jury (1996) concluded that the hitherto overlooked Millington and Quirk (1960) model

(3)
best described the measured data as compared to the classical models. Moldrup et al. (1997) combined the Penman and Millington-Quirk model approaches into the general PMQ model

(4)
and showed that m = 3 for gas diffusivity in undisturbed soils, and m = 6 for gas diffusivity in sieved, repacked soils, gave improved descriptions compared to earlier two-parameter DP models. This study also implied a significant difference between gas diffusivity in undisturbed and repacked soils and a larger soil–type dependency for gas diffusivity in undisturbed compared to repacked soils.

Troeh et al. (1982) presented a three-parameter model for more accurately curve-fitting measured DP({epsilon}) data, including a threshold value of air-filled porosity where the gas diffusivity approached zero due to interconnected water films. Although this model can fit measured data very well (Petersen et al., 1994), it should be used with great care when simulating gas diffusion and reaction in wet soils. The DP/D0 values at low air-filled porosities may appear equal to zero in a nonlogarithmic scale plot but can actually be in the range (DP/D0 > 10-4) where gas diffusion still dominates compared to solute diffusion.

More conceptually advanced DP({epsilon}) models include macroscopic pore distribution models (Nielson et al., 1984; Freijer, 1994; Steele and Nieber, 1994). These models take into account soil physical characteristics such as pore-size distribution and include several empirical and likely soil type–dependent constants. The models are valuable for understanding diffusion dependency of soil texture and structure based on calibration to measured data but are not immediately applicable for predicting DP({epsilon}) for a given soil without first carrying out gas diffusivity measurements (Freijer, 1994).

Recent work has focused on simpler and more directly applicable soil type–dependent DP({epsilon}) models, using theCampbell (1974) soil water retention parameter to describe pore-size distribution. Moldrup et al. (1996) suggested using the tortuosity term from the Burdine (1953)–Campbell (1974) unsaturated hydraulic conductivity model. This in combination with a measured reference-point value of gas diffusivity (equal to the measured DP value at the highest air-filled porosity considered in each study) gave accurate predictions of DP({epsilon}) for 16 undisturbed soils. Moldrup et al. (1999) showed that measurements of gas diffusivity or gas permeability at a single soil water potential (between -100 and -500 cm H2O), in combination with the Ball (1981a) tortuous tube gas flow model and the introduction of a soil type-dependent equivalent tube radius, significantly improved the DP({epsilon}) descriptions for six undisturbed soils representing a broad soil texture interval.

Although the need for only a single porosity (Moldrup et al., 1996) or single potential (Moldrup et al., 1999) reference-point measurement of DP much reduces the time and difficulty associated with measuring the entire DP({epsilon}) relation, any actual measurement of DP for a given soil is in practice outside the scope of most chemical-transport and fate-modeling studies, because it is experimentally involved and requires special measurement equipment.

In this study, we therefore (i) establish a predictive relation between DP and {epsilon} at a given soil water potential (reference point), (ii) insert this reference point expression in the Burdine (1953)–Campbell (1974)– Moldrup et al. (1996) relative gas diffusivity model to develop a simple DP({epsilon}) model that is fully based on the soil water characteristic (SWC) curve, and (iii) validate the new SWC-based gas diffusivity model against independent data for undisturbed surface and subsurface soils.


   Materials and methods
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
Results and discussion
 Conclusions
 REFERENCES
 
Soil cores were collected at a former manufactured-gas plant site in the city center of Hjørring, 50 km north of Aalborg in Northern Jutland, Denmark. In situ remediation for coal tar compounds has been carried out at the site since 1993. At the specific soil sampling location the soil is unpolluted throughout the vadose zone profile (depth of the vadose zone is around 10 m). The soil type is mainly loamy sand, but more finely textured horizons were identified in the 4 to 7 m soil zone during establishment of nearby groundwater monitoring wells. When a new groundwater monitoring well was installed in 1998, two large intact soil cylinders (1-m length, 0.1-m i.d.) were collected from the 4 to 5 and 6 to 7 m soil depths. A nonuniform clay pocket was observed in the upper 15 cm of the 4 to 5 m soil cylinder. The upper part of the 6 to 7 m cylinder appeared more finely textured than the lower part. We therefore focused on three 0.4-m soil horizons: the 4.2 to 4.6, 6.0 to 6.4, and 6.4 to 6.8 m horizons.

From the large soil cylinders, six smaller intact soil cores (0.034-m length, 0.061-m i.d., 100 cm3 sample volume) were collected at equal distance throughout each 0.4-m horizon. No sublayering was observed. At the sampling depths equal amounts of soil were then collected and mixed together to obtain a depth-weighted soil sample for soil texture analysis. The bulk soil was air-dried, crushed, and sieved through a 2-mm aperature sieve. The bulk soil and the 18 intact 100 cm3 soil cores (six from each 40-cm horizon) were stored in the dark at 2°C until the measurements were made.

Particle density was measured on the bulk soil by the method of Blake and Hartge (1986) and soil texture by the method of Gee and Bauder (1986). Soil water retention was measured by the method of Klute (1986). The intact soil cores were saturated in sand boxes and subsequently drained to three water potentials ({Psi}), using either a hanging water column ({Psi} = -50 and -100 cm H2O) or a pressure plate apparatus ({Psi} = -500 cm H2O). The Campbell (1974) soil water retention parameter, b, was determined as the slope of the soil water characteristic curve in a log–log coordinate plot.

Gas diffusivity (DP) was measured on the intact cores after drainage to each of the three water potentials. The experimental setup was first suggested by Taylor (1949) and further developed by Schjønning (1985a). Soil gas diffusion was measured with oxygen as the experimental gas at 20°C. Calculation with a simple oxygen consumption model using typical consumption rates from Danish subsoils showed that oxygen consumption could be considered negligible during the short periods needed to measure DP at each soil water potential. Table 1 shows the basic soil physical characteristics and Table 2 the measured soil water retention data (given as the air-filled porosity at each of the three soil water potentials), the fitted Campbell (1974) soil water retention parameter b, and the measured gas diffusivities for the three Hjørring soil layers.


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  		Table 1 Soil physical characteristics of the Hjørring soil

 

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  		Table 2 Soil water characteristics and gas diffusivities at three soil water potentials (-50, -100, and -500 cm H2O) for the Hjørring soil. The Campbell (1974) soil water retention parameter, b, is given. Numbers in parentheses are standard deviations

 
To compare gas diffusivity models, the root mean square error (RMSE) of prediction was used for best overall fit compared to the measured data

(5)
where di is the difference between the predicted and the measured value of DP/D0 at a given air-filled porosity, and n is the number of measurements.

Predicting Reference-Potential Gas Diffusivity
Schjønning et al. (unpublished data) measured gas diffusivity at -100 cm H2O of soil water potential for 113 different Danish soils and soil layers. Together with data from Ball (1981b), Heidman (1989), and Schjønning (1989), gas diffusivity measurements at -100 cm H2O were available for a total of 126 undisturbed soils and soil layers. The clay content of the 126 soils ranged between 1.6 and 23.2%, organic matter content between 0.1 and 4.1%, sampling depth between 0 and 1.8 m, and soil core volume between 100 and 227 cm3. For each soil, gas diffusivity measurements at {Psi} = -100 cm H2O were carried out on three to six (in most cases five), closely sampled (typically within 0.25 m2), undisturbed soil cores, giving a total of 752 DP measurements. Based on the similar soil core sizes and sampling and experimental procedures, it was assumed the data from the different studies could be compared. Figure 1 shows the relation between the measured gas diffusivities at -100 cm H2O of soil water potential (DP,100) and the corresponding soil air–filled porosities at -100 cm H2O ({epsilon}100). Considering the data were collected from many different soils and soil depths and represent different cultivation practices (conventional, reduced tillage, no tillage), it is surprising a very high correlation between DP,100 and {epsilon}100 was observed (coefficient of regression r2 = 0.97), yielding

(6)



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  		Fig. 1 Gas diffusivity as a function of air-filled porosity at -100 cm H2O of soil water potential. Data for 126 different soils and soil layers (752 measurements)

 
Including terms with {epsilon}100 in the second and fourth power did not increase the coefficient of regression. Using mean values of three to six closely spaced DP,100 measurements for the 126 soil layers (instead of the 752 individual DP,100 measurements) did not change the best-fit DP,100({epsilon}100) relationship (Eq. [6]) but did slightly increase the coefficient of regression (to r2 = 0.98). Equation [6] seems to accurately describe the measured data both at high and low air-filled porosities (Fig. 1). It should, however, be noted that the relative deviations of measured DP values from Eq. [6] are larger at low {epsilon}100 values (<0.1 m3 m-3), probably because DP measurements are relatively more uncertain in near-saturated soils.

In general, the high values of DP,100/D0 and {epsilon}100 in Fig. 1 represent the easily drainable sandy soils with high air-filled porosities at -100 cm H2O, while the low values are for clayey soils. Equation [6] includes a direct effect of the soil type (soil water characteristic curve) on DP,100. At {Psi} = -100 cm H2O, the air-filled pores have an equivalent pore diameter of >=30 µm. It seems that the total volume of these large pores (= {epsilon}100) largely controls the DP,100/D0 values because the DP,100 ({epsilon}100) relation is universal for different soils and soil depths (Fig. 1).

Equation [6] seems robust for predicting DP at -100 cm H2O. It may also be useful for predicting DP at a soil water content equal to natural field capacity for a wide range of soils, because field capacity will likely occur close to -100 cm H2O except for very sandy or very clayey soils (Beukes, 1987). At present, however, sufficient data to test Eq. [6] against in situ DP measurements at natural field capacity soil water content are not available. Equation [6] will instead be used as a reference-point expression in a more conceptual, SWC-based DP({epsilon}) model.

Soil Water Characteristic-Based Gas Diffusivity Model
Inserting Eq. [6] in the Burdine (1953)–Campbell (1974) relative, unsaturated hydraulic conductivity model, modified to gas diffusivity in unsaturated soil according to Moldrup et al. (1996) yields

(7)
where b is the Campbell (1974) soil water retention parameter. Equation [7] does not require a reference-point measurement of DP, but two parameters (b and {epsilon}100) related to the SWC need to be known. This means the SWC must be measured at a minimum of two, but preferably more, different soil water potentials (to estimate b), including at {Psi} = -100 cm H2O (to obtain {epsilon}100). The chosen soil water potentials should be below the air-entry potential for the soil considered, in order for the Campbell (1974) SWC model to be valid. Soil water potentials of -100 and -500 cm H2O are appropriate for most soil types (Moldrup et al., 1999).

In this study, Fick's law is assumed valid. The contribution of Knudsen diffusion is neglected because it is quantitatively important only for very fine-grained materials (Thorstenson and Pollock, 1989). Thus, a direct influence of smaller pore sizes on gas diffusion is not considered. Pore-size distribution rather than pore size is thought to influence gas diffusivity, because the pore-size distribution largely governs the connectivity and tortuosity of the air-filled pore system. In Eq. [7], this dependency of gas phase tortuosity on pore-size distribution is described by the Burdine tortuosity–connectivity term using the Campbell pore-size distribution (soil water retention) parameter, b.

Figure 2 shows the new DP({epsilon}) model principle for a clay loam soil (data from Schjønning et al., 1999). The b value is determined as the slope of the SWC curve in a log–log coordinate plot (Fig. 2a). Measurements of the SWC were available at four different soil water potentials (-30, -100, -500, and -1500 cm H2O) for six closely sampled intact soil cores. Using mean values of DP measurements on five or more closely sampled, intact soil cores largely reduced the effects of measurement uncertainty and local-scale spatial variability on gas diffusivity in undisturbed soils (Moldrup et al., 1999). The predictions by the new SWC-dependent DP model (Eq. [7]) are shown in a log(DP/D0)–log({epsilon}) coordinate plot (Fig. 2a), which yields a straight line with a slope equal to 2 + 3/b, and in a normal DP/D0–{epsilon} coordinate plot (Fig. 2b).



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  		Fig. 2 Illustration of the model parameters in the new gas diffusivity model (Eq. [7]). (a) dotted line is fitted soil water characteristic curve in a log(-{Psi})–log({theta}) plot. Straight line is predicted gas diffusivity in a log(DP/D0)–log({epsilon}) plot. (b) predicted gas diffusivity function in a normal scale plot. The air-filled porosity at -100 cm H2O ({epsilon}100) is marked. Standard deviations of both {epsilon} and DP/D0 (six closely spaced measurements) are shown. Data from Schjønning et al. (1999)

 
The new DP({epsilon}) model predicts the measured gas diffusivities for the clay loam soil well (within the SD of measured DP).


   Results and discussion
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
 Results and discussion
Conclusions
 REFERENCES
 
The new SWC-dependent DP model was tested against independent (not included in Fig. 1) gas diffusivity data for 21 soils representing a broad soil texture interval. The data are from Ball (1981a), Heidman (1989), Freijer (1994), Kruse et al. (1996), Moldrup et al. (1996), and Schjønning et al. (1999). Soils are both agricultural and forest soils. The largest data sets are from the studies by Freijer (seven soils) and Schjønning et al. (six soils). In contrast to the case for the 126 soils in Fig. 1, gas diffusivities for the 21 soils were measured at four or more soil water potentials (and thus different {epsilon} values), making it possible to test the new DP({epsilon}) model (Eq. [7]). The number of closely sampled intact soil cores varied between 2 and 18 and averaged about 6. The clay content for the 21 soils was between 1.0 and 46.3%, organic matter content between 0.1 and 5.2%, {epsilon}100 between 0.1 and 0.37 cm3 cm-3 (except for the most clayey soil where {epsilon}100 = 0.05 cm3 cm-3), sampling depth between 0 and 1 m, and undisturbed soil core size between 100 and 227 cm3. The three different DP measurement methods used (Ball et al., 1981; Schjønning, 1985; Freijer, 1994) were assumed comparable because there was no tendency to place data from one measurement method above or below other data.

Figure 3 shows the predictions of the new SWCdependent DP model compared with the measured data for six soils from Freijer (1994). The three sandier soils (Fig. 3a–c) as expected have higher {epsilon}100 values compared to the three more clayey soils (Fig. 3d–f). The new DP model (Eq. [7]) accurately predicted the measured DP values and, without any kind of model calibration to the data, gave predictions as good as the calibrated, jointed capillary tube DP model of Freijer (1994).



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  		Fig. 3 Test of the new soil water characteristic–dependent DP/D0 model (Eq. [7]) against independent gas diffusivity data for six undisturbed soils. Data from Freijer (1994)

 
Figure 4 shows the prediction of the new DP model against data for all 21 soils. The new DP model predicted the measured gas diffusivities well at both high and low air-filled porosities (corresponding to high and low DP values in Fig. 4) and for both coarsely textured (0–10% clay) and more finely textured (>10% clay) soils (Fig. 4). DP({epsilon}) data for each of the 21 undisturbed soils showed a high degree of linearity and did not encounter significant discontinuites at low air-filled porosities when plotted in a log–log scale within a range of DP/D0 > 10-4. The good model performance at low air-filled porosities (Fig. 4) supports the concept of a simple power function model without a threshold soil air–filled porosity but with SWC-dependent parameters that accurately predict gas diffusivity in natural, undisturbed soils.



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  		Fig. 4 Scatterplot comparison of predicted (Eq. [7]) and measured gas diffusivities for 21 undisturbed soils. Note logarithmic scale

 
A comparison of accuracy between the new SWC-dependent DP model and other frequently used, soil type-independent DP models is shown in Table 3 . We note that the data from Freijer (1994) were reduced to measurements at six different {epsilon} values by taking mean values at six different soil water potentials (analogous to the data in Fig. 2). Thereby, each of the 21 soils is represented by four to six DP measurements to ensure approximately the same weight for each soil in the statistical analysis. A significant increase in accuracy (lower RMSE) is obtained by introducing the reference-potential expression DP,100({epsilon}100), together with the Burdine–Campbell type expression for relative increase or decrease in DP({epsilon}). The new model (Eq. [7]) accurately predicted the observed soil-type effects on DP and gave a reduction in RSME of prediction of 83, 77, and 58% compared to the soil type–independent Penman (1940), Millington and Quirk (1960), and Millington and Quirk (1961) models, respectively (Table 3). For the four most sandy soils, the Millington and Quirk (1961) model gave predictions as good as the SWC-dependent model (Eq. [7]), but for the remaining 17 soils Eq. [7] was superior. The SWC-dependent model also performed better (39% reduction in RMSE) than the soil type–independent PMQ model by Moldrup et al. (1997). This is promising because the PMQ model was calibrated to a data set that included 15 out of the 21 soils considered here, in order to obtain the optimal value of the PMQ model constant for undisturbed soil (m = 3 in Eq. [4]).


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  		Table 3 Test of the Penman (1940), Millington and Quirk (1960, 1961) (MQ), Moldrup et al. (1997) (PMQ), and new soil water characteristic–dependent gas diffusivity (SWC-Dp) models based on root mean square error (RMSE) of prediction for 21 undisturbed soils

 
A basic difference between Eq. [7] and the classical DP({epsilon}) models is that a reference-point gas diffusivity is predicted at {Psi} = -100 cm H2O in Eq. [7]; it is predicted for dry soil conditions (at the air–filled porosity equal to the soil total porosity, {Phi} = {Phi}) in the classical models. At {epsilon} = {Phi}, the Penman (1940) model becomes DP/D0 = 0.66 {Phi} while both Millington and Quirk (1960, 1961) models become DP/D0 = {Phi}4/3 equal to the Millington (1959) model. To understand the difference in model performance, it is therefore interesting to compare the models at very high air-filled porosities close to the soil total porosity. Figure 5 shows the predictions by the Penman (1940) and the Millington and Quirk (1961) models compared to the new SWC-dependent DP model, considering DP data for which {epsilon}/{Phi} > 0.9. It is obvious that both classical models largely overpredict diffusivities at high air-filled porosities while the new SWC model satisfactorily predicts the measured data (r2 = 0.75). The SWC-dependent model (Eq. [7]) also performed better at high air-filled porosities when compared to the other one- and two-parameter DP models (Buckingham, 1904; Call, 1957; Lai et al., 1971). The effects of using the DP,100({epsilon}100) expression in combination with the Burdine–Campbell tortuosity description, Eq. [7], gives accurate predictions even when extrapolated to nearly dry soil conditions ({epsilon}/{Phi} > 0.9), while the classical soil type-independent gas diffusivity models failed to adequately describe gas diffusivity in near-dry soil (Fig. 5).



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  		Fig. 5 Scatterplot comparison of predicted soil water characteristic–dependent (SWC-dependent), Penman (1940) and Millington and Quirk (1961)(MQ), and measured gas diffusivities at high air-filled porosities ({epsilon}/{Phi} > 0.9)

 
In general for the 21 soils, the new SWC-dependent model accurately predicted DP over the whole {epsilon} interval (Fig. 4 and 5, Table 3). The Penman (1940) model overpredicted DP in the whole {epsilon} interval. The Millington and Quirk (1961) model overpredicted DP at high air-filled porosities (and performed worse than the Penman model, Fig. 5), did well predicting DP at intermediate air-filled porosities and, especially for clayey and loamy soils, underestimated DP at low air-filled porosities (typically below 0.10–0.15 m3 m-3).

The 21 soils in Fig. 4 represent surface or near-surface soils, and gas diffusivities in deep subsoils have not, to our knowledge, previously been measured. Therefore, we measured DP in the 4 to 7 m soil depth at the Hjørring former manufactured-gas plant site (Tables 1 and 2) and tested the new SWC-dependent DP model against the measured gas diffusivities. Figure 6 shows that the new DP model (Eq. [7]) also predicts the measured data well for the three subsurface soil horizons, and overall performs better than the widely used Penman (1940) and the Millington and Quirk (1961) models. The Millington and Quirk model performs well for the two highest DP values but underestimates DP greatly for the remaining seven values corresponding to air-filled porosities below 0.13 m3 m-3. The Penman (1940) model overestimates DP for all nine values (Fig. 6). Thus, similar conclusions concerning model performance for the 21 surface soils and the 3 subsurface soil horizons were reached. It is promising that the new SWC-dependent model accurately predicted the smaller values of gas diffusivity (DP/D0 < 0.02–0.05 [Fig. 2–4 and 6]), where gas diffusivity likely becomes limiting for soil aeration, plant growth (Grable and Siemer, 1968), and aerobic biodegradation of organic chemicals in contaminated soils.



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  		Fig. 6 Scatterplot comparison of predicted soil water characteristic–dependent (SWC-dependent), Penman (1940) and Millington and Quirk (1961)(MQ), and measured gas diffusivities for the three Hjørring subsoil horizons. See Table 2 for data. Note logarithmic scale

 
The presently available gas diffusivity data for undisturbed soils were measured on relatively small intact soil cores (between 100 and 227 cm3 sample volume). Although the new SWC-dependent DP model well predicts measured diffusivities in the form of mean DP values (preferably based on five or more closely sampled [0.4–0.5 m distance] intact soil cores), both small- and large-scale spatial variability may be significant (Rolston et al., 1991). Thus, gas diffusivity measurements on different sample sizes and evaluation of spatial variability and scale dependency is an important scope of future gas diffusivity research.


   Conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
 Results and discussion
 Conclusions
REFERENCES
 
A soil water characteristic– and thus pore-size distribution–dependent model for predicting gas diffusivity in undisturbed soil is presented. The model requires measurement of the SWC curve at a minimum of two different soil water potentials, including one at -100 cm H2O. It accurately predicted gas diffusivity in 21 surface–near-surface soils and 3 deep subsurface soil horizons representing a broad soil texture interval in agricultural, forest, and urban soils. The new model performed better than the widely used, soil type–independent gas diffusivity models. We therefore recommend its use in vadose zone contaminant transport and fate models, if gas diffusion and reaction simulations are to be representative for natural, undisturbed soil conditions.


   ACKNOWLEDGMENTS
 
This work was supported by the Danish Technical Research Council's research talent project entitled "New Methods for Measuring and Predicting Liquid and Gaseous Phase Transport Properties in Undisturbed Soils," the project entitled "Continuation and Evaluation of In Situ Remediation at Hjørring Former Manufactured Gas Plant Site" (funded by the Danish EPA in cooperation with NIRAS Consulting Engineers A/S), the county government of Northern Jutland, the municipal government of Hjørring, grant 5P42ESO4699 from the National Institute of Environmental Health Sciences, NIH, and the USEPA (R819658) Center for Ecological Health Research at Univ. of California-Davis. The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official view of the NIEHS, NIH, or EPA. The authors gratefully acknowledge a travel grant from the Japanese Ministry of Education, Science, Sports, and Culture (Monbushu International Scientific Research Program, Joint Res. 10044162).

Received for publication February 17, 1999.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Materials and methods
 Results and discussion
 Conclusions
 REFERENCES
 




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K. Kawamoto, P. Moldrup, P. Schjonning, B. V. Iversen, T. Komatsu, and D. E. Rolston
Gas Transport Parameters in the Vadose Zone: Development and Tests of Power-Law Models for Air Permeability
Vadose Zone J., November 20, 2006; 5(4): 1205 - 1215.
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T. G. Poulsen, P. Moldrup, S. Yoshikawa, and T. Komatsu
Bimodal Probability Law Model for Unified Description of Water Retention, Air and Water Permeability, and Gas Diffusivity in Variably Saturated Soil
Vadose Zone J., October 3, 2006; 5(4): 1119 - 1128.
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P. Cannavo, F. Lafolie, B. Nicolardot, and P. Renault
Modeling Seasonal Variations in Carbon Dioxide and Nitrous Oxide in the Vadose Zone
Vadose Zone J., August 24, 2006; 5(3): 990 - 1004.
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C. Kjaergaard, T. G. Poulsen, P. Moldrup, and L. W. de Jonge
Colloid Mobilization and Transport in Undisturbed Soil Columns. I. Pore Structure Characterization and Tritium Transport
Vadose Zone J., May 1, 2004; 3(2): 413 - 423.
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P. Moldrup, T. Olesen, S. Yoshikawa, T. Komatsu, and D. E. Rolston
Three-Porosity Model for Predicting the Gas Diffusion Coefficient in Undisturbed Soil
Soil Sci. Soc. Am. J., May 1, 2004; 68(3): 750 - 759.
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P. Moldrup, S. Yoshikawa, T. Olesen, T. Komatsu, and D. E. Rolston
Air Permeability in Undisturbed Volcanic Ash Soils: Predictive Model Test and Soil Structure Fingerprint
Soil Sci. Soc. Am. J., January 1, 2003; 67(1): 32 - 40.
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P. Moldrup, S. Yoshikawa, T. Olesen, T. Komatsu, and D. E. Rolston
Gas Diffusivity in Undisturbed Volcanic Ash Soils: Test of Soil-Water-Characteristic-Based Prediction Models
Soil Sci. Soc. Am. J., January 1, 2003; 67(1): 41 - 51.
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S. Benvenuti
Soil Texture Involvement in Germination and Emergence of Buried Weed Seeds
Agron. J., January 1, 2003; 95(1): 191 - 198.
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S. Hashimoto and M. Suzuki
Vertical distributions of carbon dioxide diffusion coefficients and production rates in forest soils
Soil Sci. Soc. Am. J., July 1, 2002; 66(4): 1151 - 1158.
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T. Olesen, J. Gamst, P. Moldrup, T. Komatsu, and D. E. Rolston
Diffusion of Sorbing Organic Chemicals in the Liquid and Gaseous Phases of Repacked Soil
Soil Sci. Soc. Am. J., November 1, 2001; 65(6): 1585 - 1593.
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P. Moldrup, T. Olesen, T. Komatsu, P. Schjonning, and D.E. Rolston
Tortuosity, Diffusivity, and Permeability in the Soil Liquid and Gaseous Phases
Soil Sci. Soc. Am. J., May 1, 2001; 65(3): 613 - 623.
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P. Moldrup, T. Olesen, J. Gamst, P. Schjønning, T. Yamaguchi, and D.E. Rolston
Predicting the Gas Diffusion Coefficient in Repacked Soil: Water-Induced Linear Reduction Model
Soil Sci. Soc. Am. J., September 1, 2000; 64(5): 1588 - 1594.
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