Soil Science Society of America Journal 66:1151-1158 (2002)
© 2002 Soil Science Society of America
DIVISION S-1—NOTES
Vertical distributions of carbon dioxide diffusion coefficients and production rates in forest soils
Shoji Hashimoto* and
Masakazu Suzuki
Lab. of Forest Hydrology and Erosion Control Engineering, Graduate School of Agricultural and Life Sciences, The Univ. of Tokyo, Bunkyo-ku, Tokyo 113-8657, Japan
* Corresponding author (shoji{at}fr.a.u-tokyo.ac.jp)
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ABSTRACT
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In this study, we developed a new method for evaluating vertical profiles of CO2 gas diffusivity and CO2 gas production in soil samples. The CO2 flux at the boundary and the steady-state CO2 gas profile are measured under two boundary gas conditions.The differential form of Fick's second law can then be used to calculate the gas diffusion coefficients and CO2 production rate. This method was applied to an undisturbed forest soil sample in the laboratory. Both gas diffusion coefficients and CO2 production rates decreased with increasing depth. The relative gas diffusion coefficients ranged between 0.03 and 0.15, and the CO2 production rates ranged between 2.1 x 10-8 and 4.7 x 10-8 kg CO2 m3 s-1 at 20°C. Unsteady changes in the CO2 concentration profile in the soil column, and flux from the soil surface were successfully simulated with these values.
Abbreviations: condition DR, drier conditions • condition WT, wetter conditions • D/D0, relative gas diffusion coefficients
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INTRODUCTION
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ACCURATE MEASUREMENTS OF CO2 emissions from soil are important for understanding the C cycle in forest systems. Emissions of CO2 from soil are the result of CO2 produced in the soil and transported to the surface. Transport of CO2 is mainly by gas diffusion and mass flow; when the difference in pressure is small, gas diffusion dominates mass flow.
Identifying the gas diffusion coefficients of a soil is essential for analyzing and modeling gas diffusion in the soil. Traditionally, gas diffusion coefficients have been evaluated in the laboratory, using nonsteady-state methods and small soil cores (Washington et al., 1994; Moldrup et al., 1996). Such methods are suitable for handling large numbers of samples, and allow control of soil-water conditions. Methods using larger, undisturbed soil samples, or in situ testing, have been proposed (Lai et al., 1976; Rolston et al., 1991; van Bochove et al., 1998; Hashimoto and Suzuki, 2000), but none allows control of environmental factors, especially water conditions.
The CO2 production in soil is strongly controlled by soil temperature and moisture (Howard and Howard, 1993; Zak et al., 1999). There are two major methods of evaluating the CO2 production in soil. One is the laboratory core method, and the other measures the CO2 efflux from the soil surface. The laboratory core method has the advantage of being able to measure the soil CO2 production at each depth at various temperature and water conditions, but has the disadvantage of disturbing the soil system. Measuring the efflux has the advantage of being able to measure the soil CO2 production without altering the soil; however, the vertical profile of the CO2 production rate cannot be measured, and environmental conditions, such as soil temperature and soil water, cannot be controlled, so there are too many factors to consider. There are a few other methods that evaluate the CO2 production in soil; these involve placing a solution in the soil or calculating the CO2 profile using gas diffusion coefficients measured in advance (De Jong and Schappert, 1972; Campbell and Frascarelli, 1980). These methods are suitable for measuring the instantaneous CO2 production, but are not reasonable for measuring the relationships between the CO2 production rate and various environmental factors.
To overcome current limitations, any new method must be able to: (i) handle larger, undisturbed soil samples, (ii) obtain continuous vertical profiles of gas diffusion coefficients and CO2 production, and (iii) allow easy control of soil-water and soil-temperature.
In this study, we developed a way of evaluating gas diffusion coefficients and CO2 production rates in soil that satisfies these requirements. The proposed method was tested using an undisturbed soil sample, and some of the experimental results are presented.
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Materials and Methods
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Theory
This method evaluates diffusion coefficients after steady-state conditions have been established in a soil sample. One-dimensional CO2 transport can be described by the following equation.
 | [1] |
where a is the volumetric air content (m3 m-3), C is the CO2 concentration (kg m-3), z is the distance (m), q is the CO2 flux (kg m-2 s-1), and Y is the CO2 production rate in soil (kg m-3 s-1). As d(aC)/dt is zero when gas and soil water concentrations are at a steady state, Eq. [1] can be rewritten as:
 | [2] |
Assuming that the main form of CO2 transport is gas diffusion, the gas flux q is described by Fick's Law as follows:
 | [3] |
where D is the gas diffusion coefficient in the soil (m2 s-1). Figure 1
shows the discretization of the measuring system. Equation [2] for each layer is approximated as:
 | [4] |
 | [5] |
 | [6] |
where 
zi is the thickness of a layer and n is the number of layers.
In this method, two different boundary conditions are imposed, and the CO2 gas concentration, Ci, and the upper and lower fluxes, q0 and qn+1, are measured. Soil temperature and soil water conditions are kept the same for the two measurements with the different boundary condition. The interval is too short for significant decomposition of organic matter, and the CO2 concentrations in the soil do not differ enough to affect microbial activity. It can be assumed that CO2 production and the gas diffusion coefficients are not different,
 | [7] |
 | [8] |
where Xa is the value of X at one boundary condition and Xb is the value at the other. The total CO2 production in soil, 
ni=1 Yi, is equal to the fluxes measured at the soil surface.
 | [9] |
Equation [7] cannot be checked directly, so the relationship, Eq. [9] was checked experimentally.
Substituting the measured values of qn and C0 in the two boundary conditions into these equations, simple equations for Y1 - Yn, D1 - Dn-1 are obtained and can be easily solved, as shown below.
 | [10] |
These equations show that the gas diffusion coefficients can be calculated using the difference in the gradients of CO2 concentration and CO2 flux from the soil surface. The large differences in the gradients of CO2 concentration are particularly important.
Y is described using the obtained gas diffusion coefficients (Di) as
This equation shows that the CO2 production in a certain layer is the difference between the flux of inflow and outflow. De Jong and Schappert (1972) also used this relationship to calculate the CO2 production at each soil depth.
Using the gas diffusion coefficient (Dx, m2 s-1) for a certain temperature (Tx, K) and pressure (Px, kPa), the gas diffusion coefficient (Dn, m2 s-1) at another temperature (T, K) and pressure (P, kPa) can be estimated as (Campbell, 1985).
 | [12] |
Consequently, under the same soil water conditions, measuring the steady CO2 profile and soil surface flux at another temperature under only one boundary condition allows estimation of the vertical profile of the CO2 production rate.
Apparatus
The system consists of a sample column with a chamber at each end, a gas circulator, and a temperature control (Fig. 2)
. The sample cylinder is 40.0 cm long, with an inner diameter of 19.5 cm. At each end of the sample cylinder there is a 10.5-cm-long chamber, of the same inner diameter, sealed with silicone. There are several holes in the upper and lower chambers. Opening or closing holes can control the boundary conditions. When all of these holes are closed, the CO2 concentration at the boundary is high. When at least two holes are open, fresh air pumped slowly into one hole leaves through the other. The atmospheric CO2 concentration is maintained at the boundary. Two boundary conditions are as follows (Fig. 3)
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Fig. 2. Schematic diagrams of (A) the measuring system, (B) the system for controlling soil water, and (C) the system for controlling soil temperature.
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CLOSED LOWER CHAMBER CONDITION
The upper end of the soil sample is kept at atmospheric CO2 concentration and the lower end is closed. (Cn = atmospheric CO2 concentration, C0 = C40cm, q0 = 0.)
OPEN LOWER CHAMBER CONDITION
The upper and lower ends of the soil sample are kept at atmospheric CO2 concentration. (Cn = C0 = atmospheric CO2 concentration.)
Measurements are first taken with a closed lower chamber, followed within 24 h by measurements with an open lower chamber.
There are ports for sampling the soil gases at depths of 10, 20, 30, and 40 cm, tensiometers (Daiki Co., Ltd. DIK-3151) at depths of 5, 15, 25, and 35 cm, and porous cups connected to flasks and an air pump, at a depth of 35 cm, to control soil-water drainage. When drying the soil, the air pump tries to pump out the air in the flasks and the air pressure in the flasks decreases. As a result, the soil water slowly drains into the flasks (Fig. 2B). Soil temperature is controlled by circulating water at a fixed temperature in tubes surrounding the sample column using a thermo pump (TOKYORIKAKIKAI Co., Tokyo, Japan) for keeping soil temperature (Fig. 2C). The soil sample reaches thermal equilibrium within 12 h of starting the thermo pump.
The end chambers are used to find the flux from the soil surface; this is a closed dynamic chamber method (Norman et al., 1997). The CO2 concentration in the chamber is measured using a CO2 analyzer (LI-COR Co. Ltd., Lincoln, NE; type 6252) and air pump (flow rate: 23.8 mL s-1) at 1-s intervals for 3 to 5 min. The CO2 flux is calculated from the rate of increase in the CO2 concentration in the chamber. Once the flux becomes constant, soil gases at various depths can be sampled using a syringe, and the CO2 concentrations can be measured using a CO2 analyzer (Hashimoto, 2002).
In this experiment, four layers were set as 0- to 10-, 10- to 20-, 20- to 30-, and 30- to 40-cm depth. The CO2 concentration of a certain layer (eg., C15cm) is calculated from the average values of the CO2 concentration at each end (eg., C15cm = [C10cm + C20cm]/2).
Soil Material and Soil Water Retention Curve
Soil material was collected at the University Forest in Chiba, Japan. The trees at the site were predominantly chamaecyparis obtusa, cryptomeria japonica, tsuga sieboldii, and quercus glauca. Undisturbed forest soil was collected by hammering a sample column with a sharpened rim into the soil. The A0 layer was included without disturbing the fresh litter on the soil. Table 1 shows the forest's location and climate, and the soil samples' properties.
After the experiments, the soil samples were cut into layers determined by the tensiometer positions (0–10, 10–20, 20–30, and 30–40 cm) and were well saturated. The relationships between soil-water suction (
, cm H2O) and soil water content were obtained by gravimetric observations during the air-drying process. The gravimetric observations were conducted one to three times a day for 7 to 17 d. However, it was difficult to measure the total weight when the soil was saturated ( = 0) because the soil samples were large. We calculated the saturated soil water content by assuming that the specific gravity of soil was 2.72 (Shuin, 1997) and the specific gravity of organic matter was 1.56 (Kawata and Kojima, 1979).
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RESULTS AND DISCUSSION
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Figure 4A-1 and 4B-1
shows measurements made of one soil sample under two suction conditions: wetter (condition WT) and drier (condition DR). The measurements were made at 
20°C. The CO2 gas concentration measurements used to determine the gas diffusion coefficient are presented in Fig. 4A-2 and 4B-2. Carbon dioxide profiles at each condition were measured two to four times at 3-h intervals. The average values were plotted. The interval between measurements under closed and open lower chamber conditions was 24 h. Under the closed lower chamber condition, the CO2 concentration at the upper soil surface was the atmospheric CO2 concentration. Under the open lower chamber condition, the CO2 concentrations at the upper and lower soil surface were both the atmospheric CO2 concentration. Fluxes from the surface of the soil are shown in Table 2. The CO2 fluxes from the surface were measured two to four times, and the average values are shown with the standard error. The differences in the total CO2 production under two boundary conditions were very small. The relationship of Eq. [9] was checked. This indicates that the CO2 productions under both boundary conditions were the same. Moreover, the soil water suction was virtually the same under two boundary conditions. This indicates that the gas diffusion coefficients were also the same under both boundary conditions. Therefore, the assumption that the gas diffusion coefficients and CO2 production rate were the same under closed and open lower chamber conditions (Eq. [7] and [8]) was valid.
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Fig. 4. Average suction profiles for wetter conditions (condition WT) and drier conditions (condition DR) (A1, B1) and the measured CO2 profiles used to determine the gas diffusion coefficents (A2, B2) and the obtained gas diffusion coefficients (A3, B3). The CO2 fluxes were calculated at each depth from the CO2 profile and the gas diffusion coefficient (A4, B4). The CO2 production rate in a certain layer is the difference between the flux of inflow and outflow (A5, B5). The CO2 profiles were measured at 0-, 10-, 20-, 30-, and 40-cm depths. The plotted values are the average values between these depths.
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The gas diffusion coefficients were calculated using these values (BFig. 4A-3, B-3). In conditions WT and DR, the gas diffusion coefficients in the upper layers were larger than those in the lower layers. There are few reports on the vertical distribution of gas diffusion coefficients in soil, especially in forest soil (Washington et al., 1994; Osozawa and Hasegawa, 1995; van Bochove et al., 1998). In both agricultural and forest soils, gas diffusion coefficients decrease with increasing depth because the overall porosity of the upper layers of soil is generally higher than that of the lower layers, and consequently the soil-water suction is usually lower in the drier upper soil. The gas diffusion coefficients obtained in this study decreased with increasing depth as expected. At each depth, the gas diffusion coefficients under condition DR were larger than those under condition WT. This is because the soil water was drained.
Figures 4A-4 and 4B-4 show the CO2 fluxes at each depth under closed conditions calculated from the CO2 concentration profile and the obtained gas diffusion coefficients. Since the lower chamber was closed, the flux at a depth of 40 cm was assumed to be zero and that the CO2 flux at each depth moved upwards. The flux at a given depth was the integral of the CO2 production in the soil below that depth. Consequently, the flux is larger at shallower points than at deeper ones. The difference in the flux at each point is the CO2 production rate in the layer (Fig. 1 and Eq. [2] and [11]). That is to say, the CO2 evolution rate in the 0- to 10-cm layer was the difference between the flux at 0 cm and that at 10 cm. In both conditions, the CO2 production rate also decreased with increasing depth and the CO2 production rate at 0 to 10 cm was very large compared with other depths. This result agrees with previous reports (Ino and Monsi, 1969; de Jong and Schappert, 1972; Campbell and Frascarelli, 1980; Scanlon and Moore, 2000). The values of the CO2 production rate per unit soil volume are of the same order of magnitude as published elsewhere (Howard and Howard, 1993; Bowden et al., 1998).
The gas diffusion coefficients obtained were compared with estimates from the Millington-Quirk model, which has been reported to give good estimates of gas diffusion coefficients (Jury et al., 1991; Moldrup et al., 1996) and the new Moldrup model, which has been reported to give better estimates (Moldrup, et al., 2000). The Millington-Quirk model is
 | [13] |
where D/D0 is the relative gas diffusion coefficient, 
is the total porosity (cm3 cm-3), and 
is the air-filled porosity (cm3 cm-3). The new Moldrup model is
 | [14] |
where 100 is the air-filled porosity at -100 cm H2O and b is the Campbell soil water retention parameter. The gas diffusion coefficient in free air can be obtained by Eq. [12] (Campbell, 1985) with values of Dx =1.39 x 10-5 (m2 s-1), Tn = 273.16 (K), Pn = 101.3 (kPa).
Figure 5
compares the measured and estimated D/D0. Compared with the Millington-Quirk model, the measured D/D0 at a depth of 20 cm was in good agreement with estimated values. However, the D/D0 was overestimated at 10 cm and underestimated at 30 cm. The values estimated with the new Moldrup model were all larger than the measured values.
Simulation of Unsteady Carbon Profiles and Surface Flux
To validate these values, we simulated the unsteady changes of gas production and movement in a soil column. Accurate evaluation of the vertical distribution of gas diffusion coefficients and the CO2 evolution rate are essential for simulating gas transport. Soil temperature was changed from 20 to 33°C (Fig. 8A) with closed lower chamber. The profiles of CO2 concentration and CO2 flux from the upper soil-surface were measured.
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Fig. 8. The change in soil temperature (A) and a comparison of simulated and measured (B) CO2 flux from the soil surface and (C) soil CO2 profiles. The lines are the simulated values.
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The CO2 transport in soil can be described by Eq. [1] and [3]. This observation was carried out under Condition DR. Figure 6 shows the relationships between soil depth and soil air content, the gas diffusion coefficient, and the CO2 production rate. The soil air content (a) was calculated from the soil retention curve, and was approximated as shown in Fig. 6. It was assumed that the air content (a) was constant during the measurement. The profile of the gas diffusion coefficients under condition DR was approximated as shown in Fig. 6. The CO2 production rate in each layer (0–10, 10–20, 20–30, and 30–40 cm) was assumed to be constant. The relationship between the CO2 production rate in soil (Y) and soil temperature was approximated by a linear equation (Fig. 7)
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Fig. 6. The relationships between soil depth and air porosity, the relative gas diffusion coefficient, and CO2 production rate.
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Fig. 7. The relationship between soil temperature and the CO2 production rate. These relationships were approximated as linear equations.
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Figure 8
compares the simulated and measured (B) CO2 flux from the soil surface and (C) soil CO2 profile. Both the CO2 concentration profile and the CO2 flux at the soil surface were accurately simulated. The temperature of the water in the tube surrounding the soil column was changed from 20 to 35°C at 22 h. The soil temperature changed slowly and stabilized at 32°C after 20 h. Corresponding with the change in soil temperature, the CO2 concentration and CO2 flux gradually rose and reached a stable state. The CO2 concentration at deeper points changed more slowly and reached a steady state later. In particular, the CO2 concentration at 30 cm temporarily became the same as that at a depth of 40 cm at 30 h. These good results indicate that this apparatus can obtain adequate values of the gas diffusion coefficients and the CO2 production rate.
CONCLUSIONS
A new method to evaluate the vertical distribution of gas diffusion coefficients and CO2 production rates in undisturbed soil samples was proposed and tested using an undisturbed sample of forest soil. The advantage of this method is that it allows measurement of the vertical distribution of gas diffusion coefficients using undisturbed soil samples and controlled soil-water and soil-temperature conditions. Moreover, the sample size is considerably larger than was possible with previous methods. These advantages will allow this experimental system to be applied to other studies, such as the movement of gas at different temperatures or before and after rainfall, or the relationships between CO2 gas diffusion coefficients and earthworm (Lumbricus terrestris) or micro-organism activity, and so on.
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ACKNOWLEDGMENTS
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The author acknowledges the input of two anonymous reviewers and the editor, whose comments improved the quality of this paper.
Received for publication May 28, 2001.
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TOP
ABSTRACT
INTRODUCTION
•: 10 cm; 
: 20 cm, 
: 30 cm, open symbols are values under wetter conditions (condition WT), and solid symbols are values under drier conditions (condition DR).