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The soil gas and solute diffusion coefficients and their dependency on soil total porosity (Φ), fluid-phase (air or water) contents, and pore-size distribution largely control chemical release, transport, and fate in soil. The diffusion coefficients hereby play a key role in both local and global environmental issues including spreading, biodegradation and volatilization of hazardous chemicals at polluted soil sites, and soil uptake, production, and emission of greenhouse gases. In a series of papers, we present new advances in describing and predicting the gas and solute diffusion coefficients in variably saturated porous media, carefully distinguishing between repacked and undisturbed media. Also, we establish direct links between gas and solute diffusivity and pore-size distribution, with further links to pore continuity and tortuosity. In this first paper, a porosity correction term is added to a recently presented model for predicting gas diffusivity in repacked soil. The obtained POrosity-Enhanced (POE) model assumes that increased Φ creates additional interconnectivity between air-filled pores. The POE model is tested against data for 18 repacked soils ranging from 0 to 54% clay, including new data measured in this study for both noncompacted and compacted, high-porosity soils. The POE model accurately predicts gas diffusivity across a wide Φ range up to 0.75 m3 m -3 , whereas the original model is accurate only for Φ up to 0.55 m 3 m -3 . A unifying, two-parameter function for gaseous phase pore continuity (f g ) is suggested. The f g function illustrates developments in gas diffusivity models during the last century, including assumptions behind the increasingly precise prediction models for repacked soil. Last, the POE model is coupled with the widely used van Genuchten (vG) soil-water characteristic model, hereby establishing an accurate and predictive link between soil gas diffusivity and pore-size distribution. The closed-form POE-vG gas diffusivity model is highly useful to evaluate effects of pore-size distribution and soil type on gas diffusivity and gas transport in repacked soil systems.

Accurate description of the soil-gas diffusion coefficient (Dp) as a function of air-filled (e) and total (Φ) porosities is required for studies of gas transport and fate processes. After presenting predictive models for Dp in repacked and undisturbed soils (Part I and II), this third paper takes a more descriptive approach allowing for the inclusion of inactive air-filled pore space, e in . Three model-based interpretations of e in are presented: (1) a simple power-law model (labeled Millington-Call) with the exponent (V) taken from Millington (1959; Science 130:100-102), and expanded with a constant e in term (= 0.1 m 3 m -3 ), (2) a model (SOLA) based on analogy with solute diffusion and assuming a linear increase in pore continuity from zero at the threshold air-filled porosity where gas diffusion ceases (e th ) to a maximum at e = Φ, (3) a power-law model (VIPS) assuming variable e in that linearly decreases from a maximum at e = e th to zero at e = Φ. Assuming e th = 0.1 m 3 m -3 , all three models satisfactorily predicted Dp in 18 repacked soils. The difference between the three models is mainly pronounced for higher-Φ soils, and each model has its own advantage. The SOLA model together with similar models for solute diffusivity allows a direct comparison of pore continuity in the soil gaseous and liquid phases, suggesting large differences in tortuosity and inactive fluid-phase between the two phases. The low-parameter Millington-Call model could account for variability in measured Dp along a field transect (Yolo, California) by varying e in with ±0.03 m 3 m -3 3 and is applicable for stochastic gas transport simulations at field scale. The mathematically flexible VIPS model highly accurately fitted D P (e) data for undisturbed soil, illustrating the large possible variations in e th and V. The VIPS model is coupled with the van Genuchten (vG) soil-water characteristic model, yielding a closed-form expression for Dp as a function of soil-water matric potential. The VIPS-vG model is useful to illustrate the combined effects of pore size distribution and inactive pore space on soil-gas diffusivity.

The soil gas diffusion coefficient (D P ) and its dependency on air-filled porosity (e) govern most gas diffusion-reaction processes in soil. Accurate D P (e) prediction models for undisturbed soils are needed in vadose zone transport and fate models. The objective of this paper was to develop a D P (e) 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 D P (e) model, (ii) the classical Buckingham (1904) model for D P at air saturation, and (iii) a recent macroporosity dependent model for D P at -100 cm H 2 O of soil-water metric potential (ψ), yielded a single equation to predict D P as a function of the actual e, the total porosity (Φ), and the macroporosity (e 100 ; defined as the air-filled porosity at ψ = -100 cm H 2 O). The new model, termed the three-porosity model (TPM), requires only one point (at -100 cm H 2 O) on the soil-water characteristic curve (SWC), compared with recent D P (e) models that require knowledge of the entire SWC. The D P (e) was measured at different ψ on undisturbed soil samples from dark-red Latosols (Brazil) and Yellow soils (Japan), representing different tillage intensities. The TPM and five other D P (e) models were tested against the new data (17 sods) and data from the literature for additional 43 undisturbed soils. The new TAM performed equally well (root mean square error [RMSE] in relative gas diffusivity

Soil-water-characteristic-dependent (SWC-dependent) models to predict the gas diffusion coefficient. D r , in undisturbed soil have only been tested within limited ranges of pore-size distribution and total porosity. Andisols (volcanic ash soils) exhibit unusually high porosities and water retention properties. The Campbell SWC model and two Campbell SWC-based models for predicting Dp in undisturbed soil were tested against SWC and Dp data for 18 Andisols and four Gray-lowland (paddy field) soils from Japan. The Campbell model accurately described SWC data for all 22 soils within the matric potential range from -10 to -15 000 cm H 2 O. The SWC-dependent Buckingham-Burdine-Campbell (BBC) gas diffusivity model predicted Dp data well within the same matric potential range for the 18 Andisols. The BBC model showed a minor but systematic underprediction of Dp for three out of the four Gray-lowland soils, likely due to a blocky soil structure with internal fissures. A recent Dp model that also takes into account macroporosity performed nearly as well as the BBC model. However, Dp in the macropore region (air-filled pores >30 μm) was consistently underpredicted, likely due to high continuity of the macropore system in both Andisols and Gray-lowland soils. In agreement with previous model tests for 21 European soils (representing lower porosities and water retention properties), both SWC-dependent D p models gave better predictions for the 22 Japanese soils than soil-type independent models. Combining Dp and SWC data, a so-called gas diffusion fingerprint (GDF) plot to describe soil aeration potential is proposed.

Soil air permeability (k a ) governs convective air and gas transport in soil. The increased use of soil venting systems during vadose zone remediation at polluted soil sites has created a renewed interest in k a and its dependency on soil type and soil air-filled porosity (e). Predictive k a (e) models have only been tested within limited ranges of pore-size distribution and total porosity. Andisols (volcanic ash soils) exhibit unusually high porosities and water retention properties. In this study, measurements of k a (e) on 16 undisturbed Andisols from three locations in Japan were carried out in the soil matric potential interval from -10 cm H 2 O (near water saturation) to -15 000 cm H 2 O (wilting point). Two simple power-function k a (e) models, both with measured k, at -100 cm H 2 O as a reference point, gave similar and good predictions of k a (e) between -10 and -1000 cm H 2 O. For one location comprising finely textured and humic Andisols, both models largely underpredicted k,(e) in dry soil (

Hydrophobic organic chemicals labeled with 14 C are often used as tracers to study chemical fate and transport in soil. Wet oxidation is the recognized but labor-demanding method used most often to measure the concentration of radioactive organic tracers in the soil. In this study, we test an alternative, simpler method for quantification of 14 C-labeled hydrophobic organic chemicals in soil samples. The soil samples were extracted directly with scintillation fluid in glass scintillation vials (Scintillation Fluid Extraction, SFE method) and were subsequently analyzed by liquid scintillation counting. Application of internal standards showed no significant quenching or reduced counts of the 14 C-labeled chemical caused by the presence of settled soil particles in the scintillation vials. Hence, the scintillation fluid could be used simultaneously as both scintillation and extraction media. Decreasing the amount of soil containing 14 C-labeled chemicals added to the scintillation vial was shown to increase the extraction efficiency of the SFE method. Aging (contact time) and concentration were shown to affect the results of the SFE method. However, in a naphthalene diffusion experiment, where aging varied between almost no contact time and 20 days and concentration of naphthalene varied between ∼0 to 40 μg g -1 , the estimated naphthalene diffusion coefficient was shown to be influenced only minimally when using the SFE method compared with the wet oxidation method. We emphasize that the SFE method is applicable only to sterile systems with no degradation or assimilation of 14 C-labeled compounds. If this condition is met and there is appropriate consideration of the effects of chemical aging and concentration, the SFE method seems to be a useful and labor-saving alternative to the traditional wet oxidation method for determination of the concentration of 14 C-labeled organic chemicals in soil samples.

Realistic models for transport of organic chemicals in soil require accurate predictions of the adsorption-desorption kinetics. In this study, a physically based two-compartment one-rate (TCOR) sorption model was evaluated by comparison of model simulations to measured adsorption-desorption isotherms of naphthalene (C 10 H 8 ) for five different soils on a short-term (48 h) and a longer-term (504 h) time scale. Two soils exhibited minor adsorption-desorption nonsingularity (labeled Type I soils), two soils pronounced nonsingularity (Type II soils), and the fifth soil pronounced nonsingularity only on the longer-term time scale (Type I/II soil). The TCOR sorption model fitted, measured adsorption-desorption isotherms well on both short-term and longer-term time scales. However, the TCOR sorption model parameters varied for each soil between short-term and longer-term data, especially for Type II soils. The uniqueness of the TCOR model fit was tested by varying the number of desorption data used, resulting in markedly changed parameter values. The TCOR sorption model was evaluated by using model parameters obtained from short-term data to predict longer-term sorption results. The TCOR prediction of adsorption-desorption behavior was good for Type I soils, satisfactory for the Type I/II soil, and poor for Type II soils. Model parameters obtained from short-term and longer-term experiments were used to predict independently measured adsorption kinetics, showing decreasing prediction accuracy with increasing sorption nonsingularity. The results imply that the TCOR sorption model description of the diffusion process at the grain scale is oversimplified, and that sorption nonsingularity is not well explained by kinetic factors alone.

Solute diffusivity (ratio of diffusion coefficients in soil and free water, D s /D 0 ) is markedly soil-type dependent. Soil texture and pore size distribution govern the threshold soil-water content (θ th ) where D S /D 0 approaches zero as a result of discontinuous diffusion pathways. In a recent study (Soil Science 161:633-645), we suggested that θ th can be predicted from the soil-water characteristic curve (SWC) based on the Campbell pore size distribution parameter, b. In this study, the θ th -b expression was recalibrated based on diffusivity data for three soils (Hiroshima sand, Foulum loamy sand, and Yolo loam) measured in this study plus 20 soils reported in the literature, obtaining θ th =0.020b. As the SWC is often not measured, a second θ th expression that requires only knowledge of soil texture and bulk density was calibrated from measured data. A third expression, including both soil texture, bulk density, and Campbell b, was also calibrated and gave the most accurate description of θ th . The solute impedance factor (ratio of diffusivity by volumetric soil-water content), f 1 = D S /(θ Do), was shown to increase linearly with the water content available for diffusion, θ a =θ - θ th . The slopes of the f 1 -θ a relations were similar for most soils and did not exhibit soil-type dependency. Based on this, a so-called constant slope impedance factor (CSIF) model to predict D S (θ a )/D 0 is presented. The model can be used in combination with any of the three suggested θ th expressions. Combined with the soil-texture/bulk-density dependent θ th expression, the model accurately predicted solute diffusivities for three independent soils for which the SWC were not known.

Predictive models for the solute diffusion coefficient, D S , dependency on volumetric soil-water content, 0, are often applied in simulations of solute transport and fate in natural, undisturbed soils. However, all available D S (θ) models have been developed from measurements on sieved, repacked soil. In this study, D S for chloride was measured in both repacked and undisturbed loamy sands at different soil-water contents. The measurements on undisturbed soil were carried out using a modified half-cell method, where the source half-cell is a sieved and repacked soil core and the other half-cell is an undisturbed soil core. Thus, the problems of (i) incomplete contact area at the interface between undisturbed half-cells and (ii) potentially different diffusion properties in undisturbed half-cells can be avoided. The modified half-cell method requires that the diffusion coefficient in sieved, repacked soil is determined separately and that the experimental data is analyzed with a numerical solution to the diffusion equation. No significant difference in chloride D S (θ) between undisturbed and sieved, repacked soil was observed for a Danish (Foulum) loamy sand and a Japanese (Hiroshima) loamy sand. A recently presented soil type dependent D S (θ) model, derived from repacked soil data, shows it to be applicable also for predicting solute diffusion coefficients in natural, undisturbed soils.

Investigations of gas transport and fate processes in packed soil systems require knowledge of the gas diffusion coefficient, D p , as a function of air-filled porosity, e. On the basis of the literature, data from six studies over the porosity range of 0.1 to nearly 1.0, it is reconfirmed that the Marshall (1959) model better predicts D p (e) in completely dry, repacked porous media than do the Penman (1940) and Millington (1959) models. The smaller D p value in wet soil, as compared with dry soil at the same air-filled porosity, is accounted for by introducing a water-induced linear reduction (WLR) term, equal to the ratio of air-filled porosity to total porosity, in the D p (e) model. By adding the WLR term in each of the three D p (e) models for dry porous media, the so-called WLR(Marshall), WLR(Penman), and WLR(Millington) D p (e) models for wet soil are developed. To test the three WLR models, D p was measured at different soil-water contents in six differently textured (6-38% clay) repacked soils. The WLR (Marshall) model accurately and best described D p (e) for all six soils and additional soils from the literature. All three WLR models performed better than previous D p (e) models. This study implies that the smaller D p in a wet soil, which is due to water-induced changes in air-filled pore shape and pore connectivity, can be described by a simple, linear function of relative air-filled porosity. The WLR(Marshall) model represents a conceptual and accurate model to predict D p (e) in sieved, repacked soil.

Time domain reflectometry (TDR) is a widely used, nondestructive measurement technique for determining soil-water content (θ) and bulk soil electrical conductivity. Until recently, small scale applications of TDR have been restricted because of the lack of small-scale, high-resolution TDR probes. As a result of the introduction of the TDR coil probe principle (Nissen et al. 1998b) and, in this study, the printed circuit board TDR probe (PCBP), the lower limit of the measurement scale for TDR is changing. The travel time of the electromagnetic waves in the PCBP was prolonged by forcing the electromagnetic waves to travel in a three-rod serpentine waveguide produced in the copper cladding of a circuit laminate (50 mm long, 10 mm width, 0.64 to 1.00 mm thickness). The apparent relative dielectric permittivity (K a ) measured by the PCBP (K a, PCBP ) was calibrated against K a measured by a standard two-rod TDR probe in air and six fluids of various K a . A two-phase dielectric mixing model was used to describe the contributions of the circuit laminate and the surrounding media to K a , PCBP . Eleven PCBPs were produced on four different types of circuit laminate with well known water absorption properties. Minor changes in K a attributable to water absorption could be observed for some of the circuit laminates. However, all four circuit laminates showed equal measurement performance during water infiltration in an initially air-dried soil. None of the circuit laminates was damaged by the soil environment during the water transport experiments. The waveguide of the PCBP is in direct contact with the soil, which should enable the PCBP to also measure electrical conductivity (EC). A calibration experiment was carried out where the load resistance (R 1 ) and the EC were measured in deionized water and six KC1 solutions by the PCBPs and a conductivity meter, respectively. A simple linear relationship was found between RL and EC. Therefore, in contrast to the TDR coil probe, the PCBP seems promising for obtaining simultaneous, small-scale and high-resolution TDR measurements of water and solute transport.

Variations of gas diffusivity (ratio of gas diffusion coefficients in soil and free air, D s /D o ) with air-filled porosity (∈) influence the transport, degradation, and volatilization of reactive gasses in soil systems. We show that the prediction accuracy of the Penman-Millington-Quirk (PMQ) diffusivity model (introduced in Part VII of this series) is often improved significantly by including as a reference point a measured value of the gas diffusion coefficient (D fc ) at a single soil-water potential, ψ, between -100 and -500 cm H 2 O. As a result, the root mean square error of prediction was reduced by 45% (based on individual D s /D o measurements) and by ≥ 65% (based on mean values of 6 to 9 closely-spaced D s /D o measurements) for undisturbed soil samples from six differently textured surface soils. Gas permeability is measured more easily and more rapidly than gas diffusivity, and we suggest that a measured value of gas permeability (k fc ) at a single soil-water potential, combined with a tortuous tube permeability model and the PMQ diffusivity model, can also be used to improve D s /D o predictions. For practical use, a relation between the equivalent tube radius (r fc ) at ψ = -100 cm H 2 O and clay content, taken to represent the soil structure-forming ability, is proposed for surface soils. Gas diffusive transport simulations using the DARC numerical model (Part I of this series) verified that the inclusion of a single (D fc or k fc ) measurement in the D s /D o (∈) predictions can improve simulation accuracy significantly. D fc - and k fc -based diffusivity models require limited measurement effort and seem promising for site-specific simulations of gas diffusion and reaction.

Accurate prediction of changes in the gas permeability during variable soil-moisture conditions is a prerequisite for improved simulation and design of soil-venting systems for removal of volatile organic chemicals in polluted soils. Air permeability, k, as a function of soil air-filled porosity

Knowledge of short-term changes in soil physical properties attributable to manure application is a prerequisite for estimating water and solute movement in manure-amended soils. Ion diffusivity and water transport characteristics were measured after the application of liquid cattle manure in two soils of different texture. Chloride diffusivity apparently decreased in a mixture of a coarse sand and 17% cattle manure compared with diffusivity in the sand without manure application. No difference was seen for a similar mixture using a sandy loam. A large dry matter content in the extracted pore liquid suggested that the coarse sand with low specific surface area only adsorbed small amounts of the added manure dry matter, explaining the increased tortuosity for ion diffusion. Addition of 15-20% manure gave a large increase in water holding capacity (0.10 cm3 cm-3 at a soil-water potential of -1500 cm H2O) and an increase of the Campbell soil-water retention parameter, b, by a factor of 3 to 4 for both soils. When manure was applied by direct injection into slits in the soil, the dry matter content of the manure controlled the rapid initial redistribution of water. A model for the relative soil-liquid sorptivity (ratio of sorptivity when applying manure, S, to sorptivity when infiltrating water, S0) as a function of manure dry matter content is proposed.

Measurements of nitrogen transformation with high temporal and spatial resolution are needed to better understand and predict nitrogen losses from manure-amended soil. Centimeter-scale measurements of nitrogen transport and transformations were carried out in a soil-manure model system corresponding to direct injection of liquid manure into soil. Influence of manure type (cattle or pig manure), initial soil-water, and soil-nitrate content were investigated. The manure type was the dominating factor with respect to both the initial redistribution of water and solutes and the subsequent nitrogen transformation processes. The liquid transport from the pig manure into the soil was rapid and extensive compared with the cattle manure. In both systems, the initial water transport created a low-nitrate zone at the manure-soil interface, possibly limiting denitrification that was found to be insignificant. Nitrification was inhibited initially in the cattle manure systems with high NH4/+ and DOC concentrations. A small N immobilization during the first 2 days of incubation, followed by a net mineralization, was seen in all experiments. An inverse Diffusion-Reaction Model (IDRM) was used to calculate spatial and temporal variations in net nitrate production rates after the initial water transport had ceased. Good agreement was found between IDRM-calculated net nitrate production rates and measured nitrification rates. The net nitrate production rates were higher in the pig manure than in the cattle manure systems in the first 8 to 10 days, but they then decreased rapidly as a result of NH4/+ limitation in the pig manure system. Unlike the frequently used mass balance considerations, the IDRM includes the effects of diffusion and, therefore, seems promising for high resolution analyses of solute transformation processes.

O2, C and N metabolism in organic hot-spots (sites where the intensity of microbial respiration creates a high O2 demand) was studied with fresh or anaerobically digested liquid cattle manure as substrates. A gel-stabilized mixture of soil and manure, 16 mm thick, was sandwiched between layers of soil with a water content adjusted to field capacity, and incubated at 15°C for up to 3 wk. When fresh manure was used, O2 microprofiles demonstrated an O2 penetration into the hot-spot of < 1 mm after 1–3 d, increasing to ca. 2 mm after 3 wk. During this time, O2 uptake rates decreased from 100–150 to ca. 50 nmol O2 cm−2 h−1. With digested manure, the lower C availability in this substrate resulted in O2 penetration depths of 3–4 mm and O2 uptake rates of

The gas diffusion coefficient in soil (D P ), 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 (e) 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 (r 2 = 0.97) for a simple, nonlinear expression describing D P at -100 cm H 2 O of soil water potential (D P,100 ) as a function of the corresponding air-filled porosity (e 100 ), equal to the volume of soil pores with an equivalent pore diameter >30 μm. A new D P (e) model was developed by combining the D P,100 (e 100 ) expression with the Burdine relative hydraulic conductivity model, the latter modified to predict relative gas diffusivity in unsaturated soil. The D P,100 and Burdine terms in the D P (e) 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 D P (e) 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 H 2 O. When tested against independent gas diffusivity data for 21 differently textured and undisturbed soils, the SWC-dependent D P (e) 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 D P (e) 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.