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Published online 11 January 2008
Published in Soil Sci Soc Am J 72:126-134 (2008)
DOI: 10.2136/sssaj2006.0101
© 2008 Soil Science Society of America
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SOIL BIOLOGY & BIOCHEMISTRY

A Subsurface, Closed-Loop System for Soil Carbon Dioxide and Its Application to the Gradient Efflux Approach

T. M. DeSuttera,*, T. J. Sauerb, T. B. Parkinb and J. L. Heitmanc

a Dep. of Soil Science, Walster Hall, North Dakota State Univ., Fargo, ND 58105, formerly with, USDA-ARS National Soil Tilth Lab., Ames, IA, 50011
b USDA-ARS National Soil Tilth Lab., Ames, IA, 50011
c Soil Science Dep., Williams Hall, North Carolina State Univ., Raleigh, NC, 27695

* Corresponding author (thomas.desutter{at}ndsu.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Carbon dioxide concentrations in the soil can vary both temporally and spatially. Methodology was developed to semicontinuously measure subsurface concentrations of CO2 using expanded, porous Teflon (ePTFE) tubing. Lengths of ePTFE tubing (7.6 m) were buried at 0.02, 0.1, and 0.18 m below the soil surface in a Harps loam soil (fine-loamy, mixed, superactive, mesic Typic Calciaquoll) in central Iowa, and also positioned directly on the soil surface (0 m). Soil atmospheric gases that diffused through the walls of the tubing were circulated in a closed-loop design through solid-state CO2 sensors to determine the concentration of CO2 at each depth. Independent measures of CO2 concentrations were also determined by sampling the in-line gas stream of the ePTFE system and from samples extracted from gas wells positioned near the buried tubing. Good agreement (r2 > 0.95) was observed between the ePTFE system and the independent measures, with the ePTFE having biases of 1.2 and 1.37 times greater than the in-line and gas well samples, respectively. The soil-gas diffusion coefficient of CO2 (Ds) was determined using intact soil cores and values were about 2.5 times less than two popular models used to predict Ds in soil. Estimates of CO2 flux using Fick's Law, six approaches to determine the vertical CO2 concentration gradient, and three methods to determine Ds ranged from >800 to <1 µmol m–2 s–1 on Day of the Year 239.5. Although Fick's Law is commonly used to estimate CO2 flux from soil, the approach used to determine the vertical CO2 concentration gradient and method used to determine Ds can both include sources of uncertainty.

Abbreviations: AFP, air-filled porosity • DOY, day of the year • ePTFE, expanded, porous Teflon • PE, ultra-high-molecular-weight polyethylene


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Numerous methods have been used to determine CO2 concentrations beneath the soil surface. Two popular methods include gas wells (Burton and Beauchamp, 1994; Davidson et al., 2006; Drewitt et al., 2005; Risk et al., 2002) and solid-state CO2 sensors (Chen et al., 2005; Hirano et al., 2003; Jassal et al., 2005; Liang et al., 2004; Tang et al., 2003, 2005; Turcu et al., 2005). Historically, gas wells used for determining CO2 concentrations were sampled infrequently (i.e., days) while the solid-state CO2 sensor can be used continuously. An advantage of the automated, continuous measurements from these solid-state sensors is that the dynamic nature of CO2 concentrations beneath the soil surface can be determined (Jassal et al., 2005; Tang et al., 2003). These solid-state sensors are fixed in a location, however, and may be susceptible to the spatial variability of soil environments. An alternative approach to address both spatial and temporal variability is to bury porous tubing in the soil and circulate the gas that has diffused from the soil atmosphere into the inner tubing volume in a closed-loop through gas analyzers (Gut et al., 1998, 1999, 2002).

A common application of soil CO2 concentration data is to estimate the flux of CO2 from the soil surface. This calculation is often made using Fick's Law:

Formula 1[1]
where F is the flux of CO2 (µmol m–2 s–1), Ds is the soil-gas diffusion coefficient of CO2 in the soil (m3 soil air m–1 soil s–1), C is the concentration of CO2 (µmol m–3), and z is the depth below the soil surface (m). Variations in estimated flux may exist from the same data set depending on the approach used to determine the vertical CO2 gradient and the model used to estimate Ds. Numerous researchers have applied Fick's Law but many times they fail to report the model used to describe the concentration with depth curve or the depth at which the concentration gradient was determined. When estimating the flux of CO2 from soil using Fick's Law, studies have either used published Ds models (Davidson et al., 2006; Drewitt et al., 2005; Hashimoto and Suzuki, 2002; Pumpanen et al., 2003; Tang et al., 2003, 2005; Turcu et al., 2005) or determined Ds values specific to their soils (Davidson et al., 2006; Hirano et al., 2003; Jassal et al., 2004, 2005; Liang et al., 2004). Jassal et al. (2005) showed mixed agreement between measured and modeled approaches for determining Ds, whereas Davidson et al. (2006) showed good agreement between a modeled and a measured approach. Underlying assumptions used in the predictive models may not be valid for all soils and can lead to errors when used to determine fluxes.

The soil gradient method has been proposed as an alternative to surface chambers for measuring CO2 flux (Hirano et al., 2003; Tang et al., 2003, 2005; Turcu et al., 2005) and may provide additional information on the CO2 production zones within the soil (Davidson and Trumbore, 1995; Drewitt et al., 2005; Fierer et al., 2005; Hashimoto and Suzuki, 2002; Risk et al., 2002; Schwendenmann and Veldkamp, 2006). The real difference (advantage) of the gradient approach is that it does not alter the soil surface boundary conditions like a chamber does. The objectives of this research were to: (i) propose and evaluate a method to semicontinuously measure CO2 concentrations beneath the soil surface using expanded Teflon (ePTFE) tubing and solid-state sensors; (ii) determine soil-gas diffusion coefficient values for CO2 using intact cores; (iii) using a simple data set, apply these measurements for calculation of CO2 efflux considering several approaches for determining the CO2 concentration gradient.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Site Description
The study site was located in central Iowa about 10 km south of Ames (41°58' N, 93°41' W) in 2005. The soil at the site was a Harps loam, which has a slope range of 0 to 2% and is classified as poorly drained. At the 0- to 18-cm depth, the soil has sand, silt, and clay concentrations of 380, 360, and 260 g kg–1, respectively, a pH of 8.2, organic C concentration of 26.2 g kg–1, a cation exchange capacity of 23.3 cmolc kg–1, and a particle density of 2600 kg m–3 (Ochsner et al., 2001). The soil bulk densities at the 0- to 0.02-, 0.02- to 0.1-, and 0.1- to 0.18-m depths were 920, 1100, and 1290 kg m–3, respectively. The soil had been managed under a corn (Zea mays L.)–soybean [Glycine max (L.) Merr.] rotation for at least 10 yr before the study. After harvest in 2004, the corn residue was chisel plowed and on DOY 126 in 2005 (6 May), the corn residue was further tilled by disking to a depth of 20 cm. Also on DOY 126 the soil was planted to soybean. The soybean was planted in 76-cm rows at a population of 310,000 seeds ha–1 and was harvested on DOY 276 (3 October).

Field Installation of Carbon Dioxide Concentration Tubing
Carbon dioxide concentrations beneath the soil surface were monitored using a modification of the Gut et al. (1998) approach. Here, a closed-loop system using 7.6-m lengths of ePTFE tubing (062404–4, W.L. Gore and Assoc., Elkton, MD) was buried at three depths on DOY 130. The ePTFE had an outer diameter and wall thickness of 9.6 and 0.94 mm, respectively, and a manufacturer-rated porosity of 60%. The tubing was white, smooth to the touch, and could be pinched using finger strength but did not collapse when buried in the soil. DeSutter et al. (2006) previously described this tubing as having a CO2 diffusion coefficient of 1.23 x 10–4 cm2 s–1 at 24°C and a 95% equilibration time (CO2 concentration inside the tubing equilibrating with the CO2 concentration outside the tubing) of <6 min.

The ePTFE tubing was installed at average depths of 0.02, 0.1, and 0.18 m below the soil surface (within the Ap horizon) using a trenching machine (Trench Master, Brown Manufacturing, Ozark, AL) equipped with a 0.36-m o.d. cutting wheel that was 0.025 m wide. A square trench (1.9 m on each side) was dug so that all four sides intersected the plant rows at a 45° angle, thereby integrating both row and interrow areas. Using modified hand tools, the 0.18-m-depth ePTFE tubing was positioned so that the center of the tube was 0.18 m below the soil surface. Soil was then backfilled for subsequent installation of tubing centered at the 0.1- and 0.02-m depths. Each end of the buried ePTFE tubing was fitted with 3.2-mm i.d. tubing that was resistant to CO2 diffusion (Bev-A-Line IV, Thermoplastic Processes, Stirling, NJ), which was then routed under the soil surface at respective depths until the instrumentation enclosure was reached. Finally, a 7.6-m length of ePTFE tubing was positioned on the soil surface (0 m) immediately above the buried tubing to assist in monitoring CO2 concentrations at the soil surface. The trenching operation provided only minor additional disturbance following the 0.2-m-deep tillage operation on the previous day. During the study, soil settling in the trench was minimal and similar to that observed in the surrounding soil.

Field Instrumentation
Gas that diffused into the inner tubing volume of the ePTFE was circulated in a closed-loop through an aboveground instrumentation suite mounted in an environmental enclosure (Fig. 1 ). Starting with the 0-m depth, the two two-way valves (ET212, Clippard Instrument Lab., Cincinnati, OH) connected to the 0-m ePFTE tubing were energized simultaneously along with the 12-V DC pump (NMP830-KNDC, KNF Neuberger, Trenton, NJ), thus completing a closed-loop. Gas flowed from the ePTFE tubing via the 3.2-mm i.d. tubing, through a six-port manifold (BHH4–06, Clippard Instrument Lab.), filter (1-µm Arco50, Pall Corp., East Hills, NY), and a Nafion air dryer (MD110–48–4, Perma Pure, Toms River, NJ) before reaching the pump. All tubing used in the environmental enclosure was resistant to CO2 diffusion and had an inner diameter of 3.2 mm (Bev-A-Line IV, Thermoplastic Processes). An air dryer, only activated when sample lines were flowing (A in Fig. 1), was used to reduce the potential for condensation within the electronics suite. From the pump, gas was routed through two solid-state CO2 sensors that had ranges of 0 to 10,000 µmol mol–1 (GMT222, Vaisala, Woburn, MA) and 0 to 100,000 µmol mol–1 (GMT221, Vaisala). Both CO2 sensors were equipped with flow-through cavities (26150, Vaisala) and were corrected for temperature and pressure effects (Tang et al., 2003). Hereafter, gas was routed through a flow meter (C-32045–18, Cole Parmer, Vernon Hills, IL), a six-port manifold, an energized two-way valve, and back into the ePTFE tubing. Gas was circulated for 120 s and the average CO2 concentration was determined during the final 60 s. After 120 s, the 0-m valves were relaxed and a two-way valve (B in Fig. 1) was energized for 120 s, which routed the gas stream through soda lime to remove CO2 from the instrumentation plumbing. This process was repeated for the 0.02-, 0.1-, and 0.18-m sampling depths once every hour for the duration of the study. The CO2 sensors were calibrated periodically when the system was not sampling using two three-way valves (C in Fig. 1) (EVO312, Clippard). The air dryer required a flow of dry gas in the opposite direction of sample flow, which was accomplished using a two-way valve, flow restrictor (MAC-A, Clippard), and compressed N2 gas. To further decrease the potential of water entering the instrument suite, water traps (100 mL each) constructed using 1.3-cm polyvinyl chloride (PVC), two barbed fittings, and two Size 0 silicone stoppers were positioned outside the enclosure near the soil surface to intercept potential liquid water. Carbon dioxide concentrations determined by the sensors were converted to mole concentrations (µmol m–3), through use of the ideal gas law, to reflect CO2 concentrations at respective soil temperatures.


Figure 1
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  		Fig. 1. Schematic diagram of the closed-loop, porous Teflon tubing and instrumentation used to determine CO2 concentrations in the soil. Valves A, B, and C control N2 gas for the air dryer, removal of CO2 from the instrumentation plumbing, and calibration of the CO2 sensors, respectively.

 
In addition, the soil atmosphere was sampled nine times during the study period using gas wells constructed of 0.08-m lengths of ultra-high-molecular-weight polyethylene (PE) tubing, which was previously described in DeSutter et al. (2006) as PE-3. Each PE tubing had an internal volume of 26 cm3. The PE tubing was fitted with 3.2-mm i.d. tubing (Bev-A-Line IV, Thermoplastic Processes) and a Swagelock union fitted with a rubber septum. Three gas wells were positioned 0.02, 0.1, and 0.18 m below the soil surface at 0, 0.19, and 0.38 m from a soybean row. From each gas well, 2 mL of sample was withdrawn and exhausted to the atmosphere to flush the dead volume in the tubing, after which 10 mL of gas sample was withdrawn from the PE and put into 6-mL gas-tight evacuated serum vials. From an in-line septum, the 0.02-, 0.1-, and 0.18-m closed-loop air streams of the ePTFE system were also sampled within the same hour as the gas wells following the same sample handling procedures. Carbon dioxide was then determined from the sample vials using gas chromatography.

Two soil water content sensors (MLx2 Delta-T Theta Probe, Dynamax, Houston, TX) were buried horizontally at the 0.06- and 0.14-m depths, 0.38 m from the plant row, and volumetric water content was estimated hourly using calibration information collected from a previous study at the site (Kaleita et al., 2005). Soil temperature was monitored at the 0.02-, 0.1-, and 0.18-m depths every hour using type-T thermocouples. An automated CO2 efflux chamber (Parkin and Kaspar, 2003) was installed within 2 m of the porous tubing. This chamber measured CO2 flux every hour, coinciding with the measurements of CO2 concentrations in the porous tubing. All instrumentation and data (both porous tube system and efflux chambers) were controlled and collected, respectively, by dataloggers (23X, Campbell Scientific, Logan, UT) and data were offloaded daily via cellular telephone. Twelve-volt DC deep cycle batteries supplemented with solar panels delivered power to the site. A 12-V DC to 24-V DC converter (AVD-34L-SW-12V, Zane International, Grand Junction, CO) was used to power the CO2 sensors. Instrumentation was operated from DOY 164 to 300.

Measurement of the Carbon Dioxide Soil-Gas Diffusion Coefficient
Intact soil cores (0.076-m i.d. by 0.076-m height) were removed from the 0.02- to 0.1- and 0.1- to 0.18-m depths in the study area from both the row and interrow locations. All cores were taken within 1.0 m of the tubing. Each core was saturated from below with tap water (25°C). After saturation was complete, cores were placed into pressure cells and pressure was applied to achieve a water potential of –4.9 kPa H2O at constant temperature (25°C) following procedures similar to those outlined by Dane and Hopmans (2002). The diffusion of CO2 through the soil was then determined on each soil core in the laboratory using modified techniques of Evans (1965) and Jassal et al. (2005) (Fig. 2 ). In our approach, a 0.6-L chamber was saturated with a known concentration of CO2 (10%) that was monitored by a solid-state CO2 sensor (0–10%, GMT221, Vaisala) (Fig. 2A). The 10% CO2 gas was used so that the concentration of gas in the headspace was greater than what was determined from soil CO2 concentrations in the field, and thus CO2 produced in the soil and introduced back into the chamber headspace was assumed to be negligible.


Figure 2
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  		Fig. 2. Instrumentation used to determine the soil-gas diffusion coefficient of CO2 through intact soil cores.

 
After CO2 saturation, the chamber was moved into place over the soil core, which was sealed to a PVC plate using a ring of modeling clay (Fig. 2B). Stopcock grease was used as both a lubricant and sealant between the two PVC plates. Thus, the only outlet for the CO2 was into and through the soil core. The concentration of CO2 in the chamber was determined and recorded every 60 s using a datalogger (21X, Campbell Scientific). The chamber was fitted with a 12-V fan, which was energized for 0.5 s min–1 to prevent CO2 gradients from occurring within the chamber.

After CO2 diffusion through the soil cores, weights of each core were recorded and the cores were resaturated. Using this method, CO2 diffusion was also determined at soil water potentials of –9.8, –49.0, and –88.4 kPa H2O. At the conclusion of these measurements, cores were dried at 105°C and reweighed to determine soil bulk density and air-filled porosity (AFP) at each water potential. The soil-gas diffusion coefficient of CO2 through the intact cores (Ds') was calculated for each soil core at each AFP following the methods outlined in Rolston (2002, Section 4.3). The SAS System Version 9.1 (SAS Institute, Cary, NC) was then used to determine the best-fit model between Ds' and AFP. This model was used to estimate Ds' in the field with AFP determined from measured water content and bulk density. The Ds' for the 0- to 0.02-m depth was estimated using the derived model with inputs of bulk density of this soil layer and the measured water content at 0.06 m.

Estimation of Soil Carbon Dioxide Efflux
As an example data set, the vertical CO2 concentration gradient was determined on DOY 237.5 to 244.5 using three approaches: (A1) a power function (y = a + bxc) was fit to CO2 concentration with depth data and the first derivative was determined at 0 and 0.02 m below the surface (TableCurve Version 4, SPSS, Chicago); (A2) linear regression was fit through the CO2 concentration with depth data and the CO2 gradient was determined using the slope of the line; and (A3) concentration data from discrete depth increments below the surface (0.02–0, 0.1–0, and 0.1–0.02 m) were used to calculate the gradient as {Delta}C/{Delta}z. Graphic examples of these three approaches are shown in Fig. 3 .


Figure 3
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  		Fig. 3. Potential methods used to determine the vertical CO2 concentration gradient in soil from actual data: (A1) dC/dz evaluated at z = zi ; (A2) slope of the line for CO2 concentration with depth; and (A3) {Delta}C/{Delta}z evaluated between zi and zj.

 
The six approximations used to determine the vertical CO2 concentration gradient were used in conjunction with three methods to determine Ds (one measured and two modeled) to estimate the efflux of CO2 according to Fick's first law of diffusion (Eq. [1]). Hourly values at midday on DOY 237, 239, 241, and 243 were chosen for this comparison, which encompassed time periods both before and after rain. Here we redefine the variables of Eq. [1] so that F is the flux of CO2 (µmol m–2 s–1), Ds is the soil-temperature-corrected CO2 soil-gas diffusion coefficient (m3 soil air m–1 soil s–1), C is the molar concentration of CO2 in the soil (µmol m–3), and z is the depth below the surface (m). The Ds' values measured from intact cores in the laboratory were adjusted to reflect the temperature dependence of the CO2 soil-gas diffusion coefficient for each estimate of CO2 flux using the approach of Fuller et al. (1966):

Formula 2[2]
where Tfield is the temperature (K) of the soil at time t, and Tlab is the temperature of the soil cores at the determination of Ds' (298.15 K). The two independent models that were used to estimate Ds were the Moldrup et al. (2000):

Formula 3[3]
and the Millington and Quirk (1961):

Formula 4[4]
where Da is the gas diffusion coefficient in free air (m2 s–1), {varepsilon}100 is the soil air-filled porosity at –100 cm H2O water potential (m3 soil air m–3 soil), {varepsilon} is the soil air-filled porosity (m3 soil air m–3 soil), b is the slope of the soil water retention curve in a log–log coordinate plot and here was 5.82, and {Phi} is the soil total porosity (m3 m–3).

Estimates of efflux were determined at 1200 h each day from DOY 238.5 to 244.5 using the six approximations of the vertical CO2 gradient and these three Ds estimates. These efflux values were compared with effluxes as determined by the automated chamber.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Semicontinuous Measurement with the Closed-Loop System
Carbon dioxide concentrations ranged from about 1 mmol mol–1 at the 0.02-m depth to >23 mmol mol–1 at the 0.18-m depth during the study period (Fig. 4A ). The 18-cm depth consistently had the greatest concentration of CO2, followed by the 0.1- and 0.02-m depths. Carbon dioxide concentrations at the 0.1- and 0.02-m depth reached maximum values of about 21 and 15 mmol mol–1, respectively, during the study. Carbon dioxide concentrations at the 0-m depth did reach values exceeding 1 mmol mol–1 but were more consistently near 0.5 mmol mol–1.


Figure 4
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  		Fig. 4. Average 24-h profiles of (A) CO2 concentration, (B) volumetric water content, and (C) temperature beneath a Harps loam soil near Ames, IA.

 
Large fluctuations in CO2 concentrations, at all but the 0-m depth, coincided with rainfall events. For example, at the 0.18-m depth, CO2 concentrations increased from about 8 mmol mol–1 on DOY 220, 1 d before a 3-d rain totaling 106 mm, to nearly 23 mmol mol–1 on DOY 225. These large increases in CO2 concentrations after rainfall events were seen at all of the subsurface depths. Maximum CO2 concentrations reached after rainfall events lagged maximum 6-cm soil moisture values by about 1.5 d (Fig. 4A and 4B). This indicates that surface sealing may not be the only factor increasing subsurface CO2 concentrations. Other researchers have also observed this pattern and have concluded that surface sealing and decreased Ds (Chen et al., 2005; Jassal et al., 2005) as well as increased microbial activity due to increased soil water content (Fierer and Schimel, 2003; Glinski and Stepniewski, 1985) may be responsible. Soil temperatures reached maximum values on about DOY 178 and steadily declined to <10°C near DOY 300 (Fig. 4C). Day-to-day temperature variations did not appear to directly influence CO2 concentrations, but an overall decline in concentration coincided with the soil temperature decline to <15°C.

Carbon dioxide concentrations determined by sampling the in-line air stream via a septum were slightly greater than concentrations determined from the in-line air stream within the closed-loop sampling scheme (Fig. 5 ). Correlation between these two independent measures were good (r2 = 0.99) but the buried-tubing method was greater by about 1.2 times with respect to all the sampling depths and sampling times. Carbon dioxide extracted from the gas wells also showed good correlation with the buried tubing (r2 = 0.95), but CO2 from the buried tubing was greater by 1.37 when comparing all sampling depths and sampling times. Differences in CO2 concentrations between the buried tubing and the in-line and gas well samples may be due to the differences in analyzing techniques. The buried-tubing gases were sampled in the field with solid-state sensors and the in-line and gas-well samples were analyzed in the laboratory using gas chromatography. Also, differences between the buried-tubing and gas-well samples may be a function of the buried tubing integrating over 7.6 m whereas the gas wells integrated over only 0.24 m (0.08 m x 3) at respective depths. Overall, good agreement was achieved between the dynamic and static sampling approaches.


Figure 5
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  		Fig. 5. Comparison of concentration of CO2 in the soil determined from the porous Teflon tubing, closed-loop design to CO2 concentrations from samples extracted from the in-line air stream of the closed-loop design and gas wells buried at 0.02, 0.1, and 0.18 m below the soil surface. Root mean square (rms) = [({Sigma} predicted values – measured values)2/number of data]0.5.

 
Carbon Dioxide Soil-Gas Diffusion Coefficient
For this soil, the approach used to determine Ds worked very well at pressures less than –88.3 kPa H2O. At pressures greater than –88.3 kPa H2O, however, soil shrinkage was significant and macropores were formed along the soil-ring interface. Average volumetric water contents at the –4.9, –9.8, –49.0, and –88.3 kPa H2O pressures were 0.41, 0.37, 0.35, and 0.33 m3 m–3, respectively. No attempt was made to seal these macropores and determine Ds values at higher pressures.

The best model fit between measured Ds and {varepsilon} was a quartic model: Ds = –1.00 x 10–8 + 3.97 x 10–5{varepsilon}4 (R2 = 0.98, SE of the model = 0.13). The two published models predicted the Ds to be about five times greater than the measured value at {varepsilon} = 0.25 m3 m–3 (Fig. 6 ), which was about the maximum {varepsilon} evaluated in this study. Overall, the Moldrup et al. (2000) and Millington and Quirk (1961) models overestimated Ds values compared with the actual and modeled Ds values. This result differs from Jassal et al. (2005), where the Millington and Quirk (1961) model tended to underestimate measured Ds values from a sandy soil.


Figure 6
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  		Fig. 6. Effect of air-filled porosity ({varepsilon}) on the soil-gas diffusion coefficient of CO2 in soil (Ds) as shown using the soil-specific, Moldrup et al. (2000), and Millington and Quirk (1961) models. Error bars are standard deviations.

 
The field Ds determined using this model ranged from about 1.5 to 5.7 x 10–7 m2 s–1 during the study period, with an average Ds of about 3.8 x 10–7 m2 s–1 (Fig. 7 ). The models of Moldrup et al. (2000) and Millington and Quirk (1961) predicted Ds values up to 2.5 times greater than the measured approach (Eq. [3]), with season-long averages near 1.1 x 10–6 and 9.3 x 10–7 m2 s–1, respectively. All models predicted sharp declines in Ds after rainfall events due to the decreased {varepsilon} of the soil.


Figure 7
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  		Fig. 7. The soil-gas diffusion coefficient of CO2 in a Harps loam soil as measured using the instrumentation in Fig. 2 and estimated using models of Moldrup et al. (2000) and Millington and Quirk (1961).

 
Vertical Carbon Dioxide Gradients
Using a curvilinear approach (Davidson et al., 2006), CO2 concentration data with depth were observed throughout the experiment but were most pronounced after rainfall events (Fig. 8A and 8B ). The power function model C = a + bzc, used to determine the vertical CO2 concentration gradient for the curve-fitting approach (A1; Table 1 ), described the curvilinear CO2 vertical concentration data very well (r2 > 0.99). The A1 approach yielded the largest vertical CO2 gradients compared with the other methods when dC/dz was evaluated at z = 0 m (Table 1). This approach yielded values ranging from 9.7 x 106 to 931.5 x 106 µmol m–3 m–1 for DOY 237.5 and 239.5, respectively. This large increase in dC/dz was the result of 32 mm of rain falling between DOY 238.29 and 238.46 (Fig. 8). Evaluating dC/dz at z = 0.02 m yielded considerably smaller gradients, where values ranged from 2.2 x 106 µmol m–3 m–1 before the rain to 3.8 x 106 µmol m–3 m–1 4 d after the rain.


Figure 8
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  		Fig. 8. Carbon dioxide concentration profiles in the soil at 1200 h between Days of the Year 237 and 244.

 

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  		Table 1. Carbon dioxide concentration gradients determined using: (A1) a curve-fitting approach where dC/dz was evaluated at z = 0 and 0.02 m; (A2) linear regression to compute the slope of the line using all data points; and (A3) using finite difference between discrete depths. Data was evaluated at 1200 h on Days of the Year (DOY) 237 through 244. Between DOY 238.29 and 238.46, 32 mm of rain was recorded at the site.

 
Using the approach of Tang et al. (2003), where the CO2 gradient was computed as the slope of the linear regression between CO2 concentration and depth (A2), gradient values were 1.6 x 106 µmol m–3 m–1 before the rain to 2.5 x 106 µmol m–3 m–1 2 d after the rain. This approach appears inconsistent with the concentration profiles that we observed (Fig. 3 and Fig. 8B). This method may be useful, however, in situations where the concentration gradient with depth is nearly linear, such as in the case of Tang et al. (2003).

The final approach used for determining the vertical CO2 gradient was the finite-difference approach (A3; Table 1). For this approach, gradients evaluated between 0.02 and 0 m were consistently greater than those computed for either 0.1 to 0 or 0.1 to 0.02 m. The peak gradient was 19.1 x 106 µmol m–3 m–1 on DOY 239.5; the gradient steadily declined to levels observed before the rainfall by DOY 244.5. The gradient from 0.1 to 0.02 m was smallest about 24 h after the rainfall (1.2 x 106 µmol m–3 m–1) and peaked at 2.2 x106 µmol m–3 m–1 on DOY 242.5, 4 d after rainfall. This decline in the gradient immediately after the rainfall was caused by similar CO2 concentrations at the 0.02- and 0.1 m depths, which provides evidence of surface sealing or increased heterotrophic and autotrophic respiration. This approach has an advantage in that only two depths are needed to determine the concentration gradient; however, curvilinear concentration with depth patterns may be undetected using this approach.

Carbon Dioxide Efflux
Irrespective of the method used to derive Ds, estimates of CO2 efflux using Approach A1 evaluated at z = 0 m overestimated efflux by about 600 times that observed with the automated efflux chamber (Table 2 ). These high estimates of efflux are out of scale with many reported values (Ham and Knapp, 1998; Jassal et al., 2005; Parkin and Kaspar, 2003; Tang et al., 2003). Approach A1 evaluated at z = 0.02 m, when combined with the two modeled Ds approaches, yielded efflux values more consistent with the automated chambers (Table 2). In contrast, efflux estimates using the measured Ds values were nearly three times lower than the effluxes determined using the automated chamber at z = 0.02 m.


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  		Table 2. Estimated CO2 efflux from a Harps loam soil using six approaches to determine the vertical CO2 gradient (Table 1) and three methods to estimate the soil-gas diffusion coefficient of CO2 in this soil (Fig. 7) and measured CO2 efflux determined by an automated sampling chamber.

 
The A2 approach underestimated efflux on all days compared with the automated chamber when using the measured Ds values, even on DOY 237.5 when the concentration profile was most linear (Table 2). Although greater estimates were observed when using the modeled Ds values, values were still less than the automated chamber except for DOY 239.5 using Moldrup et al. (2000) (Table 2). The potential error of using the A2 approach when estimating efflux follows from the fact that the assumption of a linear vertical concentration gradient is not always valid. After rainfall events, such as DOY 239.5, the concentration gradient becomes very nonlinear and this approach may greatly underestimate the concentration gradient (Fig. 8, Table 2).

Of the three finite-difference approaches for determining vertical CO2 gradients (A3), gradients evaluated between 0.02 and 0 m yielded the greatest efflux values (Table 2). The combination of this CO2 gradient and the measured Ds model gave estimates of efflux that were similar to the automated chamber except 1 d after rainfall (DOY 239.5). Here, as observed when dC/dz was evaluated at z = 0 m, the estimated CO2 efflux sharply increased when the chamber efflux decreased. Using the gradient between 0.02 and 0 m and between 0.1 and 0 m, the two modeled Ds approaches tended to overestimate efflux compared with the automated chambers on the 2 d following the rain event (Table 2). Efflux was underestimated in all cases compared with the automated chamber using all Ds approaches and evaluating the gradient between 0.1 and 0.02 m (Table 2).

Using the chamber efflux data and the A3 approach between 0.02 and 0 m, the Ds values would have needed to be 1.3 x 10–6, 7.3 x 10–8, 3.0 x 10–7, and 6.7 x 10–7 m2 s–1 for DOY 237.5, 239.5, 241.5, and 243.5, respectively, to correctly estimate the chamber efflux. Using the modeled Ds formula (Fig. 6) and the above information, estimates of the volumetric water content between 0.02 and 0 m would be 0.22, 0.44, 0.35, and 0.29 m3 m–3 for DOY 237.5, 239.5, 241.5, and 243.5, respectively; however, the 0.06-m volumetric water content data, which were used for all Ds estimates in Fig. 7, were 0.28, 0.32, 0.30, and 0.29 m3 m–3 for DOY 237.5, 239.5, 241.5, and 243.5, respectively. Clearly, the 0.06-m data were not able to accurately describe changes in surface (0–0.02-m) soil water content in this example. Surface soil water content was overestimated during periods of drying and underestimated during periods of wetting.

A critical problem of evaluating gas fluxes from the soil surface using (Eq. [1]) is getting accurate estimates of volumetric water content and AFP near the soil surface to use in the Ds models. Currently, only two methods known to us have been used to determine volumetric water content just below the soil surface (0.01 m). These are hand sampling and the dual-probe heat capacity sensor (Heitman et al., 2003; Ochsner et al., 2003; Tarara and Ham, 1997). Hand sampling can become tedious and unrealistic if hourly estimates of efflux are to be determined. Use of dual-probe heat capacity sensors, however, can provide hourly estimates of volumetric soil water content to within 0.01 m3 m–3 (Heitman et al., 2003). Assessment of the feasibility of such approaches to determine near-surface water content in combination with gradient approaches warrants further study.


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
Estimates of CO2 concentrations in the soil can be achieved using the porous tubing (ePTFE) design outlined here. The advantages of this approach are: semicontinuous, in situ measurements of CO2 concentrations with depth; use of the same sensor(s) in determining CO2 concentrations at all depths; the ability to integrate over a large area; fast equilibration between soil atmosphere and inner tubing volume; and the ability to sample the air stream for other gases. There are also numerous disadvantages, however, including: initial disturbance of the soil at installation; difficulty with size and placement of tubing near the soil surface; the need to remove water or water vapor before CO2 analysis; and the cost of the ePTFE used here, although there are less expensive alternatives (DeSutter et al., 2006).

A point of interest that should also be considered is the outside diameter of the tubing and how this may affect overall tubing depth. In this study, the center of the ePTFE tubing was positioned at the target depths of 0.02, 0.1, and 0.18 m. However, using the 0.02-m position as an example, the tubing depth ranged from 0.015 to 0.025 m below the surface, leaving 50% of the tubing above and below the target depth. Surface roughness at the time of installation may also complicate the determination of the exact tubing depth at installation. This uncertainty may affect the calculated concentration gradient and the estimate of efflux.

Although not observed in this study, trenching may alter the soil physical structure. Following heavy rains, the trenched soil may settle, have a reduction in macroporosity, and hardsetting may occur after drying (Karunatilake and van Es, 2002). These results may affect the estimates of Ds and ultimately the depth of the tubing. The soil used in this study was tilled before installation of the tubing and there was no visual evidence of soil settling. The likelihood of soil settling after trenching in undisturbed soils (i.e., prairie, forest, no-till agriculture) is great, however, and thus increased care should be taken when assessing both Ds and tubing depth in the trench compared with the surrounding soil.

Using CO2 concentration data with depth with the objective of determining CO2 efflux using Fick's Law (Eq. [1]) can be challenging. The ability to accurately estimate CO2 efflux hinges on both accurate Ds values and accurate vertical concentration gradients. Not only must gradient and Ds be estimated accurately, they must be estimated for the soil depth for which the CO2 efflux is to be calculated. For example, if CO2 efflux from the soil surface is of interest, then the Ds and dC/dz must be estimated for the surface or near-surface soil. Use of average soil profile Ds or dC/dz may not yield representative estimates of surface CO2 emissions.

Soil-specific Ds values determined for our soil were about 2.5 times less than those predicted using two popular Ds models. Thus, caution in data interpretation should be used when values of Ds are not determined independently, as done here and elsewhere using intact cores (Jassal et al., 2005) or in situ field methods (Lai et al., 1976; McIntyre and Philip, 1964; Rolston et al., 1991).

Depending on the approach used and the depth of interest, gradients may vary widely (Table 1). Determining vertical concentration gradients using linear regression was not useful after a rainfall event but may be more applicable during dry soil conditions. The finite-difference approach is the most straightforward but has the potential to misrepresent curvilinear concentration patterns with depth.

Overall, this experiment points to many questions that remain about estimating CO2 flux within and from the soil using the gradient approach. Future research is needed to improve the reliability of the gradient flux approach, including new methods for determining the Ds of surface soils (0–0.02 m), quantifying the number and placement of tubing and sensors for determining CO2 concentrations with depth, the use of automated flux chambers to help define the proper gradient approach and Ds determination, and application of sensors to determine the water content in surface soils (0–0.02 m). Even with the above concerns, the gradient approach can be a tool to estimate gas efflux or, although not a focus of this research, the most useful application of this approach may be to determine gas production zones within the soil. When using the trenching method in areas where disturbance of the soil is not possible or is impractical, aboveground chamber methods should strongly be considered.


   ACKNOWLEDGMENTS
 
Technical assistance was provided by Tim Hart, David Meek, Forrest Goodman, Paul Doi, and Jadon Kool.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
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Received for publication March 12, 2007.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 





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