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a Environmental Engineering Section, Dep. of Life Sciences, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
b City and Environment Section, Aalborg Municipality, Vesterbro 14, DK-9000 Aalborg, Denmark
c Dep. of Hilly Land Agriculture, National Agricultural Research Center for Western Region, Ikano 2575, Zentsuji, Kagawa, 765-0053 Japan
d Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Saitama, 338-8570 Japan
e Soils and Biogeochemistry, Dep. of Land, Air and Water Resources, University of California, Davis, CA 95616
* Corresponding author (pm{at}bio.auc.dk).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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) govern most gas diffusion-reaction processes in soil. Accurate DP() prediction models for undisturbed soils are needed in vadose zone transport and fate models. The objective of this paper was to develop a DP() model with lower input parameter requirement and similar prediction accuracy as recent soil-type dependent models. Combining three gas diffusivity models: (i) a general power-law DP() model, (ii) the classical Buckingham (1904) model for DP at air saturation, and (iii) a recent macroporosity dependent model for DP at –100 cm H2O of soil–water matric potential (
), yielded a single equation to predict DP as a function of the actual , the total porosity (
), and the macroporosity (100; defined as the air-filled porosity at = –100 cm H2O). The new model, termed the three-porosity model (TPM), requires only one point (at –100 cm H2O) on the soil–water characteristic curve (SWC), compared with recent DP() models that require knowledge of the entire SWC. The DP() was measured at different on undisturbed soil samples from dark-red Latosols (Brazil) and Yellow soils (Japan), representing different tillage intensities. The TPM and five other DP() models were tested against the new data (17 soils) and data from the literature for additional 43 undisturbed soils. The new TPM performed equally well (root mean square error [RMSE] in relative gas diffusivity <0.027) as recent SWC-dependent DP() models and better than typically used soil type independent models.
Abbreviations: AIC, Akaike's information criterion • BBC, Buckingham–Burdine–Campbell • Dp, soil gas diffusion coefficient • ODR, oxygen diffusion rate • RMSE, root mean square error (of prediction) • SWC, soil water characteristic curve • TPM, three-porosity model • , soil air-filled porosity
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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and soil type (texture, structure, horizon, management) control gas transport and fate in natural, undisturbed soil systems where diffusive gas transport is normally dominant compared with convective gas transport. Accurate predictive models for DP are needed to evaluate for example soil aeration (Buckingham, 1904; Taylor, 1949), the diffusion and emission of fumigants at soil fumigation sites (Call, 1957; Jin and Jury, 1995), the diffusion and volatilization of organic chemicals from polluted soil sites (Petersen et al., 1996), and the diffusion and biodegradation of greenhouse gases such as methane (Kruse et al., 1996). Numerous predictive-descriptive models for DP as a function of are available and may be divided into six groups:) models based only on . The first -based models were introduced a century ago. Edgar Buckingham, as part of his groundbreaking research on water and gas transport in soil during the period 1902–1906 at the USDA Bureau of Soils (Nimmo and Landa, 2001; Landa and Nimmo, 2003), suggested that the relative oxygen diffusion coefficient in soil was proportional to 2 (Buckingham, 1904). Other classical DP() models in the first group are the linear DP() models by Penman (1940), van Bavel (1952), and Call (1957), and the nonlinear models by Marshall (1959) and Millington (1959). The latter two can be considered mechanistically based (cutting and randomly rejoining pores) models (Ball et al., 1988; Collin and Rasmuson, 1988). ) models that take into account both and soil total porosity (). These predictive models introduce a minor soil type effect through that is dependent on for example, soil texture and management. Among the numerous models within this group are the Millington and Quirk (1960) model, as re-introduced by Jin and Jury (1996), and the Millington and Quirk (1961) model that is almost universally accepted and applied in vadose zone transport and fate models to describe both gas and solute diffusivity. The frequent use of the Millington and Quirk (1961) model is noteworthy since the model has never been validated against gas diffusivity data for undisturbed soils representing a broad interval of soil types and porosities. and , in DP() models. Since gas diffusivity in sieved, repacked soil is essentially soil type independent (Moldrup et al., 2000a, 2001), Campbell's b is considered an index to describe the effects of local scale heterogeneities in bulk density and on bulk soil DP() (Moldrup et al., 2001). Moldrup et al. (1999) combined the Campbell b dependent DP() model with the Buckingham (1904) expression for gas diffusivity in dry soil (void of water) to develop the so-called Buckingham–Burdine–Campbell (BBC) model. Moldrup et al. (2000b) further introduced the air-filled porosity at –100 cm H2O of soil–water matric potential to describe soil structure effects on gas diffusivity. ) data within the interval where measurements are available. The most frequently used within this group is the Troeh et al. (1982) model where two additional fitting parameters are introduced. The Troeh et al. (1982) model was successfully used in several studies to fit and subsequently represent measured DP() data in gas transport and fate models (Petersen et al., 1994, 1996). Although one of the Troeh et al. (1982) model parameters can be interpreted as the air-filled porosity where gas diffusion ceases due to interconnected water films (creating blocked pore space), no relationships between the Troeh et al. (1982) model parameters and soil physical properties have been identified. The model at present is descriptive rather than predictive (Moldrup et al., 2003). ) models that partition the pore space into, for example, easily accessible, difficult accessible, and nonaccessible pore space; also labeled arterial pores, marginal pores, and remote pores in the model by Arah and Ball (1994). The models have typically been developed for highly structured or highly aggregated artificial porous media or repacked soil aggregates and include the classical models by de Vries (1950) and Millington and Shearer (1971). The models contain additional pore shape and pore region parameters and are mainly descriptive models that can be used to fit detailed DP() data. ) models consists of macroscopic pore-size distribution models based on equivalent pore radius capillary tube, jointed tubes of different radii, or multidimensional capillary tube networks (Ball, 1981; Nielson et al., 1984; Steele and Nieber, 1994). Further, Freijer (1994) established interesting links between this type of model and the multiparameter Mualem–van Genuchten SWC model (van Genuchten, 1980). The DP() models in this group at present have several empirical constants that must be fitted to actual DP() data for the soil and, hence, are not immediately applicable for predicting soil gas diffusivity (Freijer, 1994).
We acknowledge that the above grouping of DP() models may be disputable since some models may arguably belong to more than one group. In general, the last three groups (IV–VI) are mainly descriptive, multiparameter DP() models that can accurately fit measured, detailed DP() data and thereby help in interpreting the data to better understand the gas diffusion process in unsaturated soil. However, the models are at present not useful for predicting DP(). Looking at the first three groups (I–III) containing predictive, low-parameter DP() models, one can conclude that there is an obvious lack of simple, predictive models that on one hand take into account soil type differences for undisturbed soils but on the other hand do not require knowledge of the entire SWC curve.
Since the entire SWC curve is normally not available or too time- and cost-consuming to measure in most vadose zone gas transport and fate studies, the objective of the present study was to develop an accurate, predictive DP() model for undisturbed soil based on a reduced SWC input requirement. Since only limited data for gas diffusivity measured on undisturbed soil samples are available, an additional goal was to present DP() data for differently managed, undisturbed soils from Brazil and Japan, and test the predictive DP() models against the new data together with DP() data for undisturbed soils from the literature.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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; the matric potential in cm H2O]). Gas diffusivity was measured on the same samples at five potentials (pF = 1.5, 1.8, 2.5, 3.0, and 3.5). The sampling area is characterized by fine-textured Latosols with typically 40 to 50% clay, 10 to 20% silt, and 30 to 50% sand. Organic C content was low, around 0.9% for the A horizon and 0.2% for the B horizon. Dominating clay minerals were kaolinite and gibbsite. The soils typically had a microaggregated soil structure. The main crop was soybean. Samples were taken at the 5- to 10-cm and 15- to 20-cm depths (A horizon) and 45- to 50-cm and 55- to 60-cm depths (B-horizon). Six closely spaced, 100-cm3 undisturbed samples (5-cm i.d., 5.05-cm length) were taken within each layer. The sampling area was divided into different sub areas with the different combinations of soil management and organic amendments (compost), see Table 1. For the tilled fields without compost, only one sampling depth (45–50 cm) within the B horizon was used. For the field plots with compost, the compost had been added for 3 yr at 20 Mg ha–1 yr–1, and soil samples were taken three months after the latest addition of compost. Since local-scale variations in both water retention and gas diffusivity were low (standard deviations <0.025 in relative soil gas diffusivity and <0.02 m3 m–3 in volumetric water content) and comparable with the study of Moldrup et al. (2003)(their Fig. 1)
, mean values of air-filled porosity and gas diffusivity was used for the six closely spaced soil samples at each soil matric potential (pF value). Differences in gas diffusivity and soil water characteristics between samples within the A horizon at each plot were small so samples at the 5- to 10- and 15- to 20-cm depths are considered to represent a single soil layer. The same is the case for the B horizon (Table 1).
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) using a hanging water column ( 
–30 cm H2O; pF 1.5) or a pressure plate apparatus ( < –30 cm H2O). After each drainage step, gas diffusivity was measured on the samples, using the same method as applied by Moldrup et al. (1996)( 2000a, 2000b, 2003). The experimental set-up (diffusion chamber) was first suggested by Taylor (1949). Soil-gas diffusion was measured at 20°C. Oxygen at atmospheric concentration was the tracer gas and analyzed as a function of time in the diffusion chamber. In brief, the diffusion chamber was flushed with 100% N2 after which the upper end of the soil core was exposed to the atmosphere. Oxygen was measured in the diffusion chamber with an oxygen electrode. Oxygen consumption in the soil core could be considered negligible during the short periods (minutes to a few hours depending on matric potential) needed to measure the soil gas diffusion coefficient at each matric potential (Moldrup et al., 2000a, 2000b; Rolston and Moldrup, 2002). The soil gas diffusion coefficient was calculated by the method of Currie (1960), also following Rolston and Moldrup (2002)(p. 1114–1121).
Models
The measured soil–water retention data were described by the Campbell (1974) SWC model (Eq. [1]).
 | [1] |
is the matric potential (cm H2O), e is the matric potential at air-entry (cm H2O), 
is the volumetric water content (m3 m–3), s is the water content at saturation (m3 m–3), and b is the Campbell pore-size distribution parameter (b > 0). Campbell b was found as the slope of the SWC curve in a log()–log(–) coordinate system.
The measured gas diffusivity data were compared with three soil-type independent and two soil-type dependent prediction models (Eq. [2]–[ 6]). The most frequently used soil-type independent gas diffusivity models are the equations suggested by Penman (1940), Eq. [2], Millington and Quirk (1960), Eq. [3], and Millington and Quirk (1961), Eq. [4],
 | [2] |
 | [3] |
 | [4] |
is the volumetric soil-air content (air-filled porosity; m3 soil air m–3 soil), and is the soil total porosity (m3 m–3).
Moldrup et al. (1999) suggested the so-called BBC soil-type dependent gas diffusivity model,
 | [5] |
2 corresponds to gas diffusivity in completely dry soil, following Buckingham (1904), and the term 2 + 3/b is an analog to the Burdine(1953)–Campbell(1974) tortuosity model for describing unsaturated hydraulic conductivity (Moldrup et al., 1996). The BBC model was developed based on DP and SWC data for 20 undisturbed soils with b values ranging from 2 to 11. The BBC model was modified by Moldrup et al. (2000b) who found a highly significant correlation (r2 = 0.97) between air-filled porosity at –100 cm H2O of matric potential (100; corresponding to the volume of soil pores with equivalent pore diameter >30 µm) and gas diffusivity at –100 cm H2O (DP,100) for 126 undisturbed soils. Using the DP/D0 expression at –100 cm H2O as reference-point gas diffusivity in combination with the Burdine–Campbell tortuosity model yielded the following 100–based model for DP(),
 | [6] |
Statistical Analyses
Three statistical measures were used to evaluate and compare the predictive gas diffusivity models. To evaluate average prediction uncertainty in DP/D0 for each combination of model and data set, RMSE of prediction was used,
 | [7] |
 | [8] |
To also account for the number of model parameters when comparing model performance for a given data set, Akaike's information criterion (AIC) was used (Akaike, 1973; Carrera and Neuman, 1986; Hwang et al., 2002),
 | [9] |
), k = 2 for the Millington and Quirk DP/D0 models (based on and ), and k = 3 for the soil-type dependent DP/D0 models. Smaller (or more negative) AIC indicates better model performance (Minasny et al., 1999).
Data Sets Used for Model Tests
Three data sets were used to test and compare DP/D0 models. (i) The first data set is from Moldrup et al. (2000b) and references therein, and represents 21 differently textured European soils, including seven Dutch soils from Freijer (1994). It is noted that the data from Freijer (1994) were reduced to DP() measurements at six different values for each soil, by taking mean values at six different matric potentials. Thereby, approximately the same weight for each soil in the statistical analysis was ensured (Moldrup et al., 2000b). Values of b and for the 21 European soils are mostly low (typically below 10 and below 0.55, respectively). (ii) The second data set is for the 17 soils from the present study (Japan and Brazil) with intermediate b and values (typically 8–15 and 0.45–0.65, respectively). (iii) The third data set is from Moldrup et al. (2003) with Japanese soils including four Gray-lowland soils and 18 Andisols (volcanic ash soils). Generally, b and values were high (typically above 10 and 0.6, and up to 40 and 0.87, respectively), and the data set includes high-organic soils.
Derivation of New Three-Porosity Model for Gas Diffusivity
To derive the new DP() model, three assumptions are applied. (i) Relative gas diffusivity (DP/D0) at air saturation ( = ) can be described by the Buckingham (1904) model, that is,
 | [10] |
(ii) Relative gas diffusivity at –100 cm H2O of soil–water matric potential can be described by the empirical equation developed by Moldrup et al. (2000b), that is,
 | [11] |
(iii) Relative gas diffusivity can be described by a single power-law function in the entire interval, that is,
 | [12] |
= ), and where X is a tortuosity–connectivity parameter. To find X, the right-hand side of Eq. [12] is set equal to the right-hand side of Eq. [11] at –100 cm H2O of soil–water matric potential ( = 100), yielding,
 | [13] |
Hence, the tortuosity–connectivity parameter (X) can be found from,
 | [14] |
) model, Eq. [12] and [14], predicts gas diffusivity as a function of three porosities, the actual , the , and the 100, and is therefore termed the TPM. The value of 100 can be found as the difference between the soil total porosity and the volumetric soil–water content at –100 cm H2O of matric potential or, alternatively, be measured directly on an undisturbed soil sample drained to –100 cm H2O of matric potential using a gas pycnometer.
At first glance, the expression for the TPM tortuosity–connectivity parameter X (Eq. [14]) including two logarithmic terms may appear slightly complicated and could be expected to yield nonrealistic values of X at given combinations of 100 and . This is tested in Fig. 1 for a broad combination of 100 and values. The tortuosity–connectivity parameter X yields values between 2 and 3 for all realistic combinations of 100 and values. For example, a dense soil with a total porosity of only 0.35 m3 m–3 (corresponding to a bulk density around 1.7 Mg m–3) would not be likely to have a macroporosity larger than 0.2 m3 m–3. Values of X between 2 and 3 would also be within the expected range of values of X in Eq. [12] for gas diffusivity in most undisturbed soils (Moldrup et al., 2001).
Although the TPM include empirically based terms, the TPM and the new X term (Eq. [14]) may be physically interpreted as follows. When the air-filled porosity equals the soil total porosity (the soil is void of water), the air-filled pore spaces are well connected (low tortuosity and high pore connectivity). In this case, the TPM (Eq. [12] and [14]) reduces to the simple Buckingham (1904) equation, equal to the air-filled porosity squared, which has been shown to well predict relative gas diffusivity in dry soil (Moldrup et al., 1999). When the soil is wet, the water causes a change of the pore shape and configuration of air-filled pores, which causes increased tortuosity and lower pore connectivity for gas transport (Papendick and Runkles, 1965; Moldrup et al., 2000a). Thus, the Buckingham model will typically overestimate gas diffusivity in wet soil (Moldrup et al., 1999), and the rate of decrease in gas diffusivity with decreasing air-filled porosity should be more pronounced in the wet soil than in the dry soil case (Moldrup et al., 2000a), in agreement with values of X > 2 (Fig. 1). The difference in X values for different soils is likely explained by that the differences in pore-size distribution and soil structure create different pore connectivities at the same air-filled porosity. Examining the X-term (Eq. [14]) suggests that the ratio of volumetric content of larger soil pores (100) to the total porosity () may largely govern this pore connectivity. Hence, when the soil–water content decreases, the relative amount (volume) of larger, arterial pores may be essential for establishing the increased connectivity between air-filled pore spaces that previously were fully or partly inactive (blocked or partly surrounded by water films) at higher water contents. In perspective, a more mechanistically based model for gas diffusivity at –100 cm H2O of soil–water matric potential ( = 100) is needed to further evaluate the predicted behavior of the TPM tortuosity–connectivity parameter, X, as a function of macro and total porosities (Fig. 1).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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) at a given matric potential (Table 1). Therefore, the compost-amended soils yielded higher Campbell b values (b between 9 and 11) compared with the soils that had not received compost (b between 7 and 9). Overall, the fitted values of Campbell b varied between 7 and 11 for the Latosols, and 8 and 23 for the Yellow soils. The values of e were typically around or above –10 cm H2O and are not provided for each soil as this parameter is not included in the SWC-dependent gas diffusivity models. Since the simple two-parameter Campbell model mostly provided good fits to the measured SWC data (Fig. 2) and the predictive gas diffusivity models (Eq. [5] and [6]) are based on Campbell b, multiparameter SWC models were not considered. Fig. 3a through 3m show the measured relative gas diffusivities for the 17 Yellow soils and Latosols. Generally, the Yellow soils exhibited lower relative gas diffusivities at a given matric potential as compared with the dark-red Latosols (see also data for relative gas diffusivities at pF 1.8 in Table 1), due to higher soil-water retention and lower air-filled porosities. Very low relative gas diffusivities were observed at all matric potentials at the 20- to 27-cm depth for the normal-plowed (NP) soil (Fig. 3d). This suggests the presence of a plow pan that would likely cause a significant decrease in soil aeration potential. However, we acknowledge that gas diffusivity measured on a bulk soil sample may not by itself adequately describe oxygen supply to plant roots and soil microorganisms, as indicated by a lack of correlation between relative gas diffusivity and oxygen diffusion rates (ODR) (e.g., Feng et al., 2002), and the local-scale (within-sample) variability of ODR measurements (Logsdon, 2003). In addition, oxygen diffusion coefficients in the soil–air and soil–water phases will both play an important role with respect to aerobic microbial activity (Schjønning et al., 2003). Thus, the TPM and other predictive models for relative gas diffusivity should not be used alone but in combination with other types of measurements to evaluate soil aeration potential.
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), against measured data is shown in Fig. 3. Also shown are predictions by the BBC model, Eq. [5], that is the closest rival to the TPM. The difference is that the BBC model requires a Campbell b value, typically found from several points on the SWC between –10 and –3000 cm H2O, while the TPM only requires an 100 value corresponding to only one point on the SWC. It could be argued that the Campbell b value could instead be estimated from soil texture (Moldrup et al., 1999) but detailed soil texture information are not always available (e.g., for none of the soils in this study) and it is much less involved to measure 100 than to carry out a complete soil particle-size analysis.
The two DP() models well predicted measured gas diffusivities for the seven Yellow soils depicted in Fig. 3a through 3g, including the top layers at both tillage treatments with high gas diffusivities and high macro and total porosities (Fig. 3a and 3e) and the plow sole in the normally plowed field with very low gas diffusivities, low macroporosity, and low total porosity (Fig. 3d). The largest deviation between model-predicted and measured relative gas diffusivity (DP/D0) was 0.03 for the top layer of the ultra-deep plowed Yellow soil at high air-filled porosities (Fig. 3a); otherwise deviations were mostly <0.015.
The TPM and BBC models also gave similar predictions (deviation between model-predicted relative gas diffusivities typically <0.015) for the Brazilian dark-red Latosols. Figure 3h through 3m shows predictions and data for a selected depth within both the A-horizon and B-horizon. All three tillage treatments (no-plow, heavy disk harrow, disk plow), and both soils with and without compost amendments for the heavy disk harrow and disk plow treatments are represented. The disk-plow treatment without compost represented the least accurate model predictions among the 17 soils, with a deviation between model-predicted and measured relative gas diffusivity (DP/D0) of 0.03 to 0.05 (Fig. 3j). The reasons for this are not clear and the results for the 15- to 20-cm depth were in much better agreement with both predictive models (not shown). Only DP() model predictions with input parameter values for soil without compost amendment are shown, since model predictions with input parameter values for soil with compost amendment gave very similar results (deviation between model-predicted relative gas diffusivities <0.01).
Since the data from this study mainly represents finely textured soils, it is also interesting to compare model performance for soils spanning a broader soil texture interval. Figure 3n through 3p shows TPM and BBC model predictions for three Dutch soils from Freijer (1994). Sample scale and measurements method are comparable with the ones used in this study, as discussed by Moldrup et al. (2000b). Both models gave similar and adequate predictions for both the sandy, silty and clayey soils (Fig. 3n–3p), with the exception of the two gas diffusivities measured on air-dry, clayey soil (Fig. 3p; at close to 0.6) where the models largely overpredicted measured DP/D0.
Expanding the model test, Fig. 4
shows a test of five predictive DP() models against three data sets. Root mean square error of prediction (Eq. [7]), bias (Eq. [8]), and AIC (Eq. [9]) are shown for each combination of model and data set in Fig. 4.
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The Millington and Quirk (1960) model, Eq. [3], generally overestimated the measured gas diffusivities for all soil types (Fig. 4d–4f). For example, Eq. [3] overpredicted all measurements for the Yellow soils and Latosols in this study (Fig. 4e). The tendency for overprediction is evident also at low relative gas diffusivities (<0.02–0.05) where gas diffusivity likely becomes limiting for soil aeration (Glinski and Stepniewski, 1985).
The Penman (1940) model, Eq. [2], largely overestimated gas diffusivities for all 60 soils in the three data sets (not shown). The Penman (1940) model yielded values of RMSE between 0.095 and 0.109, bias between 0.097 and 0.100, and AIC between –167 and –296, clearly providing the worst model performance among the six models tested.
Overall, the Penman (1940) and Millington and Quirk (1960) DP() models are not recommended for use in gas transport and fate models representing natural, undisturbed soil systems. The Millington and Quirk (1961) model may often provide reasonable predictions for more sandy and lower porosity soils but cannot be trusted across soil types and porosities. The AIC values for the three soil-type independent DP() models were much higher than for the three soil-type dependent models so the use of a soil-type dependent gas diffusivity model is strongly recommended.
The three soil-type dependent DP() models, the BBC model (Eq. [5]), the original macroporosity (100) dependent model (Eq. [6]), and the new TPM (Eq. [12] and [14]), all gave reliable predictions (RMSE < 0.03, bias between 0 and –0.01) across soil types and porosities (Fig. 4g–4o). However, a small tendency for model underestimation (small, negative bias) was seen for eight out of the nine test cases (Fig. 4g–4o). The minor decrease in average prediction accuracy (0.002–0.007 higher RMSE value) for the TPM as compared with the best performing model would probably not be significant in relation to most applications in vadose zone transport and fate models. The average prediction accuracy as obtained from the calculated RMSE values is strikingly similar for the three data sets, that is, 0.014 to 0.027 in relative gas diffusivity (DP/D0). This must be considered highly accurate, also considering the inherent measurement uncertainty in DP/D0 (Rolston and Moldrup, 2002).
The TPM model did not perform best (based on AIC values) for any of the three data sets. However, the AIC ranking was 100–based model–TPM–BBC for the first data set, and BBC–TPM–100–based model for the second and third data sets. This suggests that the objective of developing a predictive DP/D0 model (the TPM) with less labor intensive input data requirement that performs at the same level as recent SWC-dependent gas diffusivity models has been met.
Figure 5
shows the relation between the Campbell pore-size distribution parameter b and the TPM tortuosity–connectivity parameter X. As expected from DP() data for undisturbed soil, X is decreasing with increasing b, that is, X is smaller for finer-textured soils (Moldrup et al., 2001, 2003). There is not a clear relationship between X and b, likely because b represents the entire pore-size distribution while X, being a function of the macroporosity (100), is more defined by the larger, arterial pores that to some extend will dominate diffusive gas transport (Arah and Ball, 1994). All X values are between 2 and 3, confirming the initial model analysis in Fig. 1.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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) model, the Millington and Quirk (1961) model performed best (overall lowest AIC and RMSE and least tendency to general over or underestimation) but could not provide reliable predictions across soil types and total porosities.
Only soil-type dependent DP() models were capable of giving realistic predictions of gas diffusivity in undisturbed soils across soil types. Both SWC-dependent models recommended in Rolston and Moldrup (2002), Eq. [5] and [6], gave reliable predictions, even when tested for a wider range of soil types and total porosities.
The new TPM that requires only one measurement point on the SWC also offered reliable predictions of DP() in undisturbed soils, with AIC and average prediction accuracy in between those of the two other SWC-dependent models. For cases where detailed SWC information are not available, the TPM (Eq. [12] and [14]) is therefore recommended for use in gas transport and fate models for undisturbed soil systems.
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ACKNOWLEDGMENTS |
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Received for publication May 12, 2003.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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