Gas transport enhancement under windy condition in poorly tilled seedbed of clayey rotational paddy field

ABSTRACT

Gas exchange between soil and atmosphere governs the growth of plants and global circulation of the gaseous component of air. Enhancement of gas exchange by wind has been reported in media with large pores. In clayey paddy fields, large aggregates (clods) and inter-aggregate pores are prone to be formed by tillage. However, the effect of wind on gas transport has not been considered in such fields. This study quantified the wind-induced gas movement through the paddy soil layer composed of large clods. The applicability of the analysis using the gas diffusion equation was also verified regarding the mean clod size and wind condition. Undisturbed soil columns were taken from the ‘poorly tilled’ and ‘fairly tilled’ paddy field under the cultivation of soybean. The mean diameters of the clods were 3.4 and 1.9 cm for the ‘poorly’ and ‘fairly’ tilled columns, respectively. A repacked silica sand column was also prepared as a reference. Diffusion tests were conducted for the columns in the field under natural wind and in the laboratory under calm conditions, with CO₂ as a purge gas and atmospheric oxygen as a tracer gas. The gas transfer efficiency was evaluated by $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$, which is the ratio of the time until the oxygen concentration reaches 50% and 90% of that in the atmosphere in the field to that in the laboratory, respectively. The results showed that gas transfer through the paddy soil layers, comprised a few centimeters of clods, under natural wind was up to 11 times quicker than under the calm conditions. The wind-induced gas exchange remained at maximum under the wind speed of more than 1.2 m s⁻¹ at 20 cm above the soil surface in the poorly tilled soil. In contrast, in the fairly tilled soil, the effect of wind gradually increased with wind speed and finally became close to that in the poorly tilled soil at the wind speed around 2.0 m s⁻¹. The applicability of the gas diffusion equation deteriorated as the wind speed increased from 1.2 to 2.6 m s⁻¹ or the mean aggregate size increased from 1.9 to 3.4 cm.

KEY WORDS:

• Clayey rotational paddy field
• poorly tilled seedbed
• gas movement
• enhancement
• wind

1. Introduction

The processes of gas exchange between the soil and the atmosphere affect not only biomass production but they are also important from the environmental perspective (Stępniewski, Stępniewska, and Rożej 2011). As an importance in crop production, oxygen exchange supports the respiration of crop roots, and water vapor transfer controls the water content near the dry soil surface, which destines the germination of crop seeds. Simultaneously, the emission of greenhouse gases, such as methane or nitrous oxide from cultivated soil to the atmosphere is also controlled by the transfer rate through the soil layer.

Although gaseous transfer in the soil can occur by several mechanisms (Hillel 1998), gas movement in the soil is usually regarded as a process of molecular diffusion because the importance of other mechanisms, such as mass flow, aerodynamic dispersion, or the pressure fluctuation of air, are relatively very low. By combining Fick’s law and the equation of continuity, the gas diffusion equation is obtained to yield solutions for the temporal distribution of gas concentration (Fujikawa and Miyazaki 2005). Numerous applications of the gas diffusion equation or the diffusion coefficient to the analysis of gas exchange between the soil and the atmosphere are found in soil science, crop science, civil engineering, earth science, etc.

In contrast, researchers have demonstrated that wind enhances the gas movement in highly permeable porous media. Studies on wind-induced gas transport in soil have a history of more than a half-century. Fukuda (1955) and Farrell, Greacen, and Gurr (1966) have left pioneering theoretical works on this phenomenon. Because the air velocity in soil follows Darcy’s law, the parabolic partial differential equation with respect to the air pressure becomes the fundamental equation for this phenomenon. Fukuda (1955) solved the equation assuming an infinitesimal boundary. However, Farrell, Greacen, and Gurr (1966) analyzed the situation with the bottom of permeable soil at a finite depth, presenting that wind gustiness had a higher effect on the air movement than the infinitesimal case. Scotter and Raats (1969) extended these studies to the relationship between oscillating air movement and the hydrodynamic dispersion of water vapor. Ishihara, Shimojima, and Harada (1992) later differentiated the type of wind-induced gas transport. They showed ‘pressure pumping’ as the major mechanism in a porous material with low air permeability, such as sand with a particle diameter of 0.2 or 0.5 mm. Simultaneously, aerodynamic dispersion dominates in porous materials with high air permeability, such as glass beads with a particle diameter of 10 mm. They also showed both mechanisms can be described in the form of Fick’s law.

Although numerous studies in the field support the validity of the diffusion and dispersion equation for the gas movement in soil with large particles under wind (e.g., Kimball and Lemon 1971; Clements and Wilkening 1974; Pourbakhtiar et al. 2017; Laemmel et al. 2019), some in situ experiments demonstrate the equation is not applicable depending on the conditions. Among such studies, Levintal, Dragila, and Weisbrod (2019) reported that the simple diffusion (dispersion) type equation could not be applied to cases of large aggregates or strong wind. They insisted that the advection-diffusion equation was more adequately fitted to the measured temporal profiles of the tracer gas concentration under such conditions, while the theoretical evidence for applying this equation to the profile has not been clearly discussed.

Large aggregates (or clods) are often formed in paddy fields (Takahashi et al. 1999; Sato et al. 2003). Especially in the fields with heavy clay soil, tilth highly depends on the soil moisture condition and cultivation history. Once the large aggregates are formed, they inhibit stable germination of seeds, and upward liquid water flows to maintain crop growth. Simultaneously, the inter-aggregate pores facilitate water vapor transfer and enhance the evaporative loss of soil moisture that maintains crops. Although such a huge pore structure also affects the movement of other gases, the effect of wind on gas flux has not been considered in the numerical estimation, even if the soil has not been sufficiently fragmented by tillage.

This study quantified wind-induced gas movement through the paddy soil layer having the macroscopic soil structure formed by tillage. To quantify the wind effect, undisturbed soil samples taken in the paddy field were placed in the soil layer of the field under natural wind, and in the laboratory under calm conditions, to measure the exchange rate of oxygen in air and CO₂ as the purging gas. The applicability of the analysis using the gas diffusion (dispersion) equation was also discussed with respect to the mean aggregate size and the wind condition.

2. Materials and Methods

2.1. Preparation of soil samples

Both poorly and fairly tilled soils were sampled from two experimental plots of a clayey rotational paddy field with different cropping histories in Niigata prefecture, Japan (37.12 N, 138.27 E), managed by the National Agricultural Research Center (NARO). Table 1 shows the cropping history and soil texture of the plots. Although slight differences were observed in the soil texture between the plots, we assumed that the soil exhibited the same intrinsic properties but different physical properties, particularly in terms of water transport and retention. Because the mean diameter of clods formed via tillage decreased gradually by the serial cropping of soybean (Takahashi et al. 1999), sampling plots were selected based on the cultivated crop in the previous year. Therefore, the plot for sampling the poorly tilled soil was planted with flooded rice in the previous year, whereas for sampling, the fairly tilled soil was planted with soybean. Tillage was conducted on May 27 or 28, 2019, and soil sampling was conducted on May 28. The samples were obtained from the surface of the plowed layer using cylindrical polyvinyl chloride (PVC) columns with a diameter of 15.4 cm and a height of 9.7 cm. As a control, Mikawa silica sand (Mikawa silica sand 8, Mikawa Quartzite, Japan) was packed into the PVC columns with a gravimetric water content of 0.10 and a bulk density of 1.35 g cm⁻³, resulting in a volumetric water content of 0.14. Based on the product’s datasheet, 99.8% and 26.0% of the sand particles were sieved through a 150-μm- and 75-μm-meshed sieve, respectively. Three replicates of soil columns were prepared for each soil sample. The bulk density, porosity, volumetric water content, and air-filled porosity are listed in Table 1. Because the effect of intra-clod pores on the wind-induced gas movement was considered to be much smaller than that of inter-clod pores, the volumetric water contents of three kind soil were not adjusted.

Table 1. Cropping history, soil texture, and soil physical properties (mean ± S.D.)

	Cropping in previous year	Soil type (ISSS)	Clay (%)	Silt (%)	Sand (%)	Bulk density (g cm^−3)	Porosity	Volumetric water content before the series of measurements	Volumetric water content after the series of measurements	Air-filled porosity^3)
Poorly tilled soil	Flooded rice	Light Clay	42.9 ± 2.8	37.7 ± 1.9	19.4 ± 3.7	0.68 ± 0.02	0.74 ± 0.01	0.32 ± 0.01^1)	0.26 ± 0.01^2)	0.49 ± 0.02
Fairly tilled soil	Soybean	Light Clay	43.0 ± 0.7	29.5 ± 2.9	27.5 ± 2.3	0.89 ± 0.02	0.66 ± 0.01	0.25 ± 0.01^1)	0.20 ± 0.02^2)	0.47 ± 0.02
Mikawa silica sand	N/A	Sand	1.3 ± 0.1	0.0 ± 0.0	98.7 ± 0.1	1.35 ± 0.00	0.49 ± 0.00	0.14 ± 0.00^2)	0.06 ± 0.01^2)	0.43 ± 0.01

1) Estimated from the weight of the soil column recorded after each measurement

2) Directly measured from the sample

3) After the end of the series of measurements

2.2. Experimental apparatus for measuring gas transfer efficiency

Figure 1 shows a schematic illustration of the experimental apparatus for the gas transfer efficiency measurement; the apparatus was constructed with reference to Scotter and Raats (1968) and Pourbakhtiar et al. (2017).

Figure 1. Schematic of the experimental setup for gas transfer efficiency measurement.

Previous studies on the measurement of the gas diffusion coefficient in porous media applied variable combinations of the purge gas and tracer gas. Although oxygen diffusion into the porous media purged by nitrogen has been the most popular (Osozawa 1998), buoyancy or solubility in water was also considered in selecting gases in this study. Scotter and Raats (1968), Pourbakhtiar et al. (2017), and Poulsen et al. (2017) used CO₂ as the purge gas and oxygen as the tracer gas because they thought the effects of the buoyancy-driven flow would have occurred if they had used N₂ gas for initial purging the experimental columns. Alternatively, Levintal, Dragila, and Weisbrod (2019) used air enriched with 2000 ppm CO₂ to fill the experimental columns and monitored the CO₂ concentration as the tracer gas because they thought this concentration had no bias due to the buoyancy-driven flow of CO₂ as the tracer and CO₂ high solubility in the water had no impact as all experiments were conducted under dry conditions. Laemmel et al. (2017) chose helium as the purge and tracer gas because it is an inert gas and its solubility in water is negligible, and the diffusion coefficient in the air is large, while the monitoring of the gas concentration is realized by constructing the elaborate sampling device and the microgas chromatograph. Considering the advantages and difficulties of these methods, this study monitored O₂ concentration moving from the air into the soil columns as the tracer gas, and CO₂ gas was used for the purge gas to mitigate buoyancy-driven upward mass flow mentioned by Pourbakhtiar et al. (2017). Although CO₂ high solubility in soil water should have caused the apparent retardation of CO₂ movement, the influence could be canceled by using the relative gas transfer parameters defined in the following sections. A detailed discussion of this issue is provided in Appendix 2.

An empty cap was attached to the lower end of the soil column to create a space for supplying CO₂ gas to fill up the soil column. The space had a height of 2.9 cm and was separated from the soil column with a perforated metal board containing 3 mm holes (aperture ratio: 51%). Oxygen sensors (SO-220; Apogee Instruments, USA) were installed at depths of 4.7 and 11.7 cm via the tubes with lengths of 2.0 cm and internal diameters of 0.5 cm. The oxygen sensors were connected to a data logger (CR1000; Campbell Scientific. Inc., USA), which recorded every 1 s. A thermocouple was incorporated into the oxygen sensor, and the oxygen concentration was corrected by the temperature based on the ideal gas law. The sensor’s response time, i.e., when the sensor sensed 90% of the actual gas concentration, was 14 s. In addition to this delay, the distance from the column to the sensor caused a difference in the O₂ concentration between the column and the sensor. To estimate this delay, numerical analysis of the O₂ diffusion in the connection tubes of the sensors was performed using the numerically obtained solutions for the temporal changes of O₂ concentration at 4.7 and 11.7 cm deep as the boundary conditions. The details of this analysis are provided in Appendix 1. As a result, the time until the O₂ concentration at the sensor reached the same value as that at the wall of the column almost fell within the range of 13 ± 1.5 s regardless of the elapsed time and the air exchange rate in the columns. Thus, 27 s, i.e., 14 s for the sensors’ response time and 13 s for the diffusion in the connecting tubes, was subtracted from the elapsed time corresponding to each measurement to correct these time lags.

2.3. Procedure for measuring gas transfer efficiency

First, the top of the column was closed with a lid, which contained valves and an oxygen sensor. Subsequently, CO₂ gas was injected into the lower space to replace the soil air in the column with CO₂ completely. The oxygen concentration in the column was monitored to confirm the replacement. After a complete replacement, the lid was removed to allow the exchange of CO₂ and air, and the oxygen concentrations at 4.7 and 11.7 cm deep were continuously measured. The measurements were performed until the output from the oxygen sensors was stabilized for more than 10 min. Then, by assuming that the O₂ concentration obtained in the previous 10 min corresponded to that of the atmosphere (i.e., 21%), the output of each sensor was calibrated.

2.4. Environmental conditions during measurements of gas transfer efficiency

In situ gas transfer efficiency measurements were conducted from June 4 to 14 June 2019, in the clayey rotational paddy field where fairly tilled soil was sampled. The field measured 30 m × 100 m, and the experiments were conducted near the center of the field under soybean cultivation. Double-lined ridges with a height of 24 cm and a top width of 30 cm were formed, but the soybean had not been established to cover the soil surface. The schematic of the in situ measurement is shown in Figure 2. The soil column was placed on a tray with a bottom size of 38.5 cm × 26.0 cm, which was installed in the ridge by excavating it, and the height of the soil column was equaled to that of the top of the original ridge. Considering the column size and the oxygen sensor length, the dimensions of this tray was suitable for putting the experimental apparatus. This procedure is important for placing the soil column under natural wind conditions in the field. The wind speed ($\mathrm{U}$) 20 cm above the soil column was measured every 1 s during the measurement by an ultrasonic anemometer (CYG-81000; R. M. Young Company, USA), which was connected to a data logger (CR1000; Campbell Scientific. Inc., USA). An example of the temporal change in $\mathrm{U}$ during the measurement is shown in Figure 3. Each column was measured two or three times under various wind conditions, and seven measurements were conducted for each soil type. Average wind speed ($\bar{U}$) and wind speed standard deviation of each measurement is summarized in Table 2.

Table 2. Wind speed ($\mathrm{U}$) during the in-situ measurement (mean ± S.D.)

	Experimental run	$\mathrm{U}$ (m s^−1) corresponded to
		$\mathrm{R}{\mathrm{t}}_{50}$ at 4.7 cm	$\mathrm{R}{\mathrm{t}}_{50}$ at 11.7 cm	$\mathrm{R}{\mathrm{t}}_{90}$ at 4.7 cm	$\mathrm{R}{\mathrm{t}}_{90}$ at 11.7 cm
Poorly tilled soil	P1	1.2 ± 0.5	1.3 ± 0.5	1.2 ± 0.5	1.2 ± 0.5
	P2	1.4 ± 0.7	1.4 ± 0.7	1.4 ± 0.7	1.5 ± 0.7
	P3	0.9 ± 0.4	1.4 ± 0.7	1.3 ± 0.6	1.7 ± 0.8
	P4	1.8 ± 0.6	2.1 ± 0.8	2.1 ± 0.8	1.8 ± 0.8
	P5	1.6 ± 0.5	1.8 ± 0.6	1.8 ± 0.6	2.0 ± 0.7
	P6	2.0 ± 0.8	1.9 ± 0.8	2.0 ± 0.9	2.1 ± 0.9
	P7	2.6 ± 0.7	2.6 ± 0.8	2.6 ± 0.8	2.6 ± 0.8
Fairly tilled soil	F1	1.3 ± 0.6	1.1 ± 0.6	1.0 ± 0.5	1.0 ± 0.5
	F2	1.5 ± 0.5	1.3 ± 0.5	1.1 ± 0.5	1.2 ± 0.6
	F3	1.2 ± 0.5	1.2 ± 0.5	1.2 ± 0.5	1.2 ± 0.5
	F4	1.2 ± 0.5	1.3 ± 0.5	1.3 ± 0.5	1.3 ± 0.5
	F5	1.8 ± 0.7	1.8 ± 0.7	1.7 ± 0.7	1.7 ± 0.7
	F6	1.5 ± 0.6	1.7 ± 0.7	1.8 ± 0.7	1.8 ± 0.7
	F7	2.0 ± 0.7	1.9 ± 0.7	2.0 ± 0.7	2.0 ± 0.7
Mikawa silica sand	M1	2.1 ± 0.7	1.9 ± 0.7	1.7 ± 0.7	1.7 ± 0.7
	M2	2.2 ± 0.8	2.2 ± 0.8	2.0 ± 0.7	1.9 ± 0.7
	M3	2.1 ± 0.8	2.1 ± 0.8	1.9 ± 0.8	1.9 ± 0.8
	M4	2.1 ± 0.8	2.1 ± 0.8	2.0 ± 0.8	2.0 ± 0.8
	M5	2.1 ± 0.8	2.2 ± 0.9	2.1 ± 0.8	2.0 ± 0.8
	M6	2.2 ± 0.9	2.3 ± 0.9	2.3 ± 0.9	2.3 ± 0.9
	M7	2.6 ± 0.9	2.5 ± 0.9	2.5 ± 0.9	2.5 ± 0.9

Figure 2. Schematic of the in situ measurement. (a) Side view (b) Sectional view.

Figure 3. An example of temporal change in wind speed ($\mathrm{U}$) during the in situ measurement.

After completing the in situ measurements, the samples were subjected to the measurements in the closed laboratory. Because the measured wind speed of 2 m height in the laboratory during 1 hour was only 0.08 ± 0.03 m s⁻¹ (mean ± S. D.), the laboratory was considered to be under calm conditions. The measurements were repeated three times for each soil column.

2.5. Determination of gas transfer efficiency

The gas transfer efficiency in the soil can be simply evaluated based on the time until the oxygen concentration at depths of 4.7 and 11.7 cm reached a certain percentage of that in the atmosphere. Pourbakhtiar et al. (2017) applied the time (‘breakthrough time’) until the oxygen concentration at a given depth reached 50% of that in the atmosphere to analyze the effect of wind on gas movement in the soil. Levintal, Dragila, and Weisbrod (2019) used the time (‘aeration time’) until the CO₂ concentration decreased to 10% of the initial one in the column. This study evaluated ${\mathrm{t}}_{50}$ and ${\mathrm{t}}_{90}$ defined as the time until the oxygen concentration at 4.7 and 11.7 cm deep reached 50% and 90% of that in the atmosphere, respectively. ${\mathrm{t}}_{50}$ and ${\mathrm{t}}_{90}$ corresponded to breakthrough time and aeration time, respectively. The relative gas transfer parameter: $\mathrm{R}{\mathrm{t}}_{50}$ or $\mathrm{R}{\mathrm{t}}_{90}$, defined as the ratio of ${\mathrm{t}}_{50}$ or ${\mathrm{t}}_{90}$ in the in situ experiments to that in the laboratory experiment was used to analyze the effect of wind on the gas transfer.

2.6. Determination of molecular diffusion coefficient and apparent gas diffusion coefficient

Based on the study by Ishihara, Shimojima, and Harada (1992), gas movement near a soil surface enhanced by wind can be mathematically described in the form of Fick’s law, as shown in Equation (1)(1) ${\mathrm{q}}_{\mathrm{w}}=-{\mathrm{D}}_{\mathrm{w}}\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{z}}$(1) , regardless of the mechanism of pressure pumping, i.e., via wind-induced pressure fluctuations or aerodynamic dispersion.

(1) ${\mathrm{q}}_{\mathrm{w}}=-{\mathrm{D}}_{\mathrm{w}}\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{z}}$(1)

where ${\mathrm{q}}_{\mathrm{w}}$ is the gas flux induced by wind (cm s⁻¹), ${\mathrm{D}}_{\mathrm{w}}$ is the wind-induced gas transfer coefficient (cm² s⁻¹), $\mathrm{C}$ is the gas concentration (cm³ cm⁻³), and $\mathrm{z}$ is the depth (cm). Because molecular diffusion, which is also represented by Fick’s law, is the other driving force of the gas movement, Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) governs the temporal change in O₂ concentration if the wind-induced gas transfer follows Equation (1):

(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2)

where $\mathrm{a}$ denotes the air-filled porosity, and D_a is the apparent gas diffusion coefficient or gross gas transfer coefficient (cm² s⁻¹) defined as

(3) ${\mathrm{D}}_{\mathrm{a}}={\mathrm{D}}_{\mathrm{m}}+{\mathrm{D}}_{\mathrm{w}}$(3)

Here, D_m denotes the molecular gas diffusion coefficient (cm² s⁻¹). ${\mathrm{D}}_{\mathrm{w}}$ should have been a function of depth because the effect of wind turbulence depends on depth, theoretically (Pourbakhtiar et al. 2017). However, because the optimal form of ${\mathrm{D}}_{\mathrm{w}}(\mathrm{z})$ could not be selected explicitly, ${\mathrm{D}}_{\mathrm{a}}$ was assumed to be constant throughout the soil layer.

To obtain the optimum ${\mathrm{D}}_{\mathrm{a}}$ that reproduces the measured temporal changes in the O₂ concentration, Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) was solved repeatedly by changing ${\mathrm{D}}_{\mathrm{a}}$ with the explicit finite difference method. For the laboratory measurement, the following boundary and initial conditions were used to solve Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) :

(4) ${\mathrm{q}}_{\mathrm{u}}=\mathrm{K}(0.21-\mathrm{C})(\mathrm{z}=0,\mathrm{t}>0)$(4)

(5) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{z}}=0(\mathrm{z}=12.6,\mathrm{t}>0)$(5)

(6) $\mathrm{C}=0(0\le \mathrm{z}\le 12.6,\mathrm{t}=0)$(6)

where ${\mathrm{q}}_{\mathrm{u}}$ is the gas flux through the upper boundary of the soil column (cm s⁻¹) and $\mathrm{K}$ is the gas transfer coefficient on the upper boundary (cm s⁻¹). However, for the in situ measurement, because the possible decrease in the O₂ concentration in the atmosphere due to the downward flux should be compensated readily by wind, the following upper boundary condition was used:

(7) $\mathrm{C}=0.21(\mathrm{z}=0,\mathrm{t}>0)$(7)

The computational domain was partitioned into an upper soil layer (0–9.7 cm deep), and a lower void space (9.7–12.6 cm deep). The grid interval $\mathrm{\Delta }\mathrm{z}$ was set between 0.7 and 1.0 cm, and the time interval $\mathrm{\Delta }\mathrm{t}$ was set to 0.5 or 1 s, considering the stability of the calculation. For the lower void space, the gas diffusion coefficient in air (${\mathrm{D}}_{\mathrm{o}}$), which was measured using an empty column, was applied for the calculation.

The root-mean-square error (RMSE) between the measured and fitted oxygen concentrations at depths of 4.7 and 11.7 cm were used as the criteria, as follows:

(8) $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left\{{{(\mathrm{C}}_{\mathrm{m}}^{\mathrm{i}}\left(4.7\mathrm{c}\mathrm{m}\right){-\mathrm{C}}_{\mathrm{c}}^{\mathrm{i}}\left(4.7\mathrm{c}\mathrm{m}\right))}^2{+(\mathrm{C}}_{\mathrm{m}}^{\mathrm{i}}\left(11.7\mathrm{c}\mathrm{m}\right){-\mathrm{C}}_{\mathrm{c}}^{\mathrm{i}}\left(11.7\mathrm{c}\mathrm{m}\right){)}^2\right\}}$(8)

where $\mathrm{N}$ is the number of observations; ${\mathrm{C}}_{\mathrm{m}}^{\mathrm{i}}$ and ${\mathrm{C}}_{\mathrm{c}}^{\mathrm{i}}$ are the measured and calculated oxygen concentrations at the i-th observation, respectively (cm³ cm⁻³). The RMSE was evaluated from the onset of measurement until the oxygen concentration at 11.7 cm deep reached 90% of that in the atmosphere.

For the experiments to induce molecular diffusion without soil using the empty column, the optimum ${\mathrm{D}}_{\mathrm{o}}$ and $\mathrm{K}$ were simultaneously determined to minimize the RMSE. Then, under the optimum $\mathrm{K}$, ${\mathrm{D}}_{\mathrm{a}}$ that minimized the RMSE was chosen as the optimum apparent gas diffusion coefficient. Based on the minimum RMSE, the diffusion model applicability was tested for each experimental condition.

To compare the measured ${\mathrm{D}}_{\mathrm{a}}$ with ${\mathrm{D}}_{\mathrm{o}}$ or ${\mathrm{D}}_{\mathrm{m}}$, temperature correction was performed for ${\mathrm{D}}_{\mathrm{o}}$ and ${\mathrm{D}}_{\mathrm{m}}$ as follows (Bitteli, Campbell, and Tomei 2015):

(9) ${\mathrm{D}}_{\mathrm{o}}({\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}})={\mathrm{D}}_{\mathrm{o}}({\mathrm{T}}_{{\mathrm{D}}_{\mathrm{o}}})({\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}}/{\mathrm{T}}_{{\mathrm{D}}_{\mathrm{o}}}{)}^{1.75}$(9)

(10) ${\mathrm{D}}_{\mathrm{m}}({\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}})={\mathrm{D}}_{\mathrm{m}}({\mathrm{T}}_{{\mathrm{D}}_{\mathrm{m}}})({\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}}/{\mathrm{T}}_{{\mathrm{D}}_{\mathrm{m}}}{)}^{1.75}$(10)

where ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}}$, ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{o}}}$, and ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{m}}}$ are the temperatures (K) during the measurements of ${\mathrm{D}}_{\mathrm{a}}$, ${\mathrm{D}}_{\mathrm{o}}$, and ${\mathrm{D}}_{\mathrm{m}}$, respectively. For the laboratory measurements, the mean temperature between 4.7 and 11.7 cm deep during the measurement was used as ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}}$, i.e., ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{m}}}$, and ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{o}}}$. For the in situ measurement, the averaged air temperature observed at a weather station located approximately 100 m from the experimental plots was applied as ${\mathrm{T}}_{{\mathrm{D}}_{\mathrm{a}}}$ because the temperatures measured by the oxygen sensors in the columns were probably higher than the actual soil temperature because of direct exposure of sunlight to the oxygen sensors.

2.7. Determination of air permeability

After measuring the gas transfer efficiency, the air permeability was measured under three different gas flow rates using the apparatus shown in Figure 4. First, N₂ gas was injected into the empty cap attached to the lower end of the soil column, and the flow rate of N₂ gas was measured using a gas flowmeter (FD-A100; Keyence, Japan). Next, the differential gas pressure between the top and bottom of the soil column was measured using a differential pressure sensor (PDT101; Vaisala Oyj, Finland, for poorly and fairly tilled soil specimens; GC30; Nagano Keiki Co., Ltd., Japan for Mikawa silica sand specimens). Finally, the air permeability was calculated using Darcy’s law, as follows (Hamamoto et al. 2009):

(11) ${\mathrm{k}}_{\mathrm{a}}=\frac{\mathrm{Q}}{\mathrm{A}}\frac{{\eta }_{\mathrm{a}}\mathrm{L}}{\mathrm{\Delta }\mathrm{P}}$(11)

Figure 4. Schematic of the experimental setup for air permeability measurement.

where ${\mathrm{k}}_{\mathrm{a}}$ is the air permeability (cm²), $\mathrm{Q}$ is the flow rate (cm³ s⁻¹), $\mathrm{A}$ is the cross-sectional area of the soil column (cm²), ${\eta }_{\mathrm{a}}$ is the viscosity (=1.82 × 10⁻⁵ Pa s, which is the value at 20°C), $\mathrm{L}$ is the height of the soil column (cm), and $\mathrm{\Delta }\mathrm{P}$ is the differential air pressure between the top and bottom of the soil column (Pa). The measured ${\mathrm{k}}_{\mathrm{a}}$ values are shown in Table 3. The ${\mathrm{k}}_{\mathrm{a}}$ in the poorly and fairly tilled soils were three and two orders higher than that in the Mikawa silica sand, respectively. Notably, because the measurement range of the differential pressure sensor was ±60 Pa and its accuracy was 0.4% span, the measured $\mathrm{\Delta }\mathrm{P}$ (> 0.7 Pa) was within than the sensor’s accuracy.

Table 3. Air permeability of soils (mean ± S.D.)

	Air permeability (${\mathrm{k}}_{\mathrm{a}}$) (μm^2)
Poorly tilled soil	(1.7 ± 0.6) × 10^4
Fairly tilled soil	(3.4 ± 1.0) × 10^3
Mikawa silica sand	9.6 ± 1.0

2.8. Determination of clod size distribution

After performing all measurements, the soil aggregates (clods) in the columns were sieved into six sizes, i.e., 5, 4, 3, 2, and 1 cm openings. The dry weights of each size class were measured to determine the tilth. The clod size distribution can be approximated using the Rosin–Rammler equation as follows:

(12) $\mathrm{R}(x_{\mathrm{p}})=100\mathrm{e}\mathrm{x}\mathrm{p}\{-(x_p/x_e{)}^n\}$(12)

The mean clod diameter ${\mathrm{x}}_{\mathrm{m}}$ (cm) can be calculated as

(13) $x_{\mathrm{m}}=x_e\mathrm{\Gamma }(1/\mathrm{n}+1)$(13)

where ${\mathrm{x}}_{\mathrm{p}}$ is the opening of the sieve (cm); $\mathrm{R}({\mathrm{x}}_{\mathrm{p}})$ is the cumulative weight of clods larger than ${\mathrm{x}}_{\mathrm{p}}$ (%); ${\mathrm{x}}_{\mathrm{e}}$ (cm) and $\mathrm{n}$ are fitting parameters; $\mathrm{\Gamma }$ is a gamma function defined as (Takahashi et al. 1999)

(14) $\mathrm{\Gamma }\left(\mathrm{s}\right)=\underset{0}{\overset{\mathrm{\infty }}{\int }}{\mathrm{e}}^{-x}{x}^{\mathrm{s}-1}\mathrm{d}x\left(\mathrm{s}>0\right)$(14)

Figure 5 shows the clod diameter distribution and mean clod diameter of the poorly and fairly tilled soils. As expected, the mean clod diameter of the poorly tilled soil was larger than that of the fairly tilled soil.

Figure 5. Clod diameter distribution of the poorly and fairly tilled soil. The error bars represent standard deviations. The mean clod diameter is shown in brackets in the legend (mean ± S.D.).

3. Results and discussion

3.1. Effect of wind on gas transfer efficiency

Figure 6 shows the relationship between the average wind speed ($\bar{U}$) at 20 cm above the soil surface and $\mathrm{R}{\mathrm{t}}_{50}$ or $\mathrm{R}{\mathrm{t}}_{90}$. In the Mikawa silica sand, $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ was larger than unity at depths of 4.7 and 11.7 cm in almost all cases. Before the onset of the in situ measurement, i.e., when the Mikawa silica sand was packed, the volumetric water content was 0.14 (Section 2.1). However, because of desiccation during the in-situ measurements, the volumetric water content was decreased to 0.06 (Table 1) at the end of the laboratory measurement. Therefore, ${\mathrm{D}}_{\mathrm{m}}$ was increased, and a faster gas exchange occurred in the laboratory measurements compared to the in situ measurements, resulting in $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ larger than unity. Additionally, the correlation between $\bar{U}$ and $\mathrm{R}{\mathrm{t}}_{50}$ or $\mathrm{R}{\mathrm{t}}_{90}$ was not significant. Consequently, the wind speed did not positively affect the gas movement in the Mikawa silica sand. This result is consistent with Fuchs and Hadas (2011), who demonstrated that wind speed did not affect the resistance of 0.2–1 mm aggregates to water vapor transport.

Figure 6. Relationship between $\bar{U}$ and $\mathrm{R}{\mathrm{t}}_{50}$ (the ratio of ${\mathrm{t}}_{50}$ at the in-situ experiment to that in the laboratory experiment) at (a) 4.7 and (b) 11.7 cm deep and relationship between $\bar{U}$ and $\mathrm{R}{\mathrm{t}}_{90}$ (the ratio of ${\mathrm{t}}_{90}$ at the in-situ experiment to that in the laboratory experiment) at (c) 4.7 and (d) 11.7 cm deep.

In the fairly tilled soil, both $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ were smaller than unity and decreased gradually with the increase in $\bar{U}$. Additionally, significant negative relationships were exhibited between $\bar{U}$ and $\mathrm{R}{\mathrm{t}}_{50}$ at 11.7 cm deep, and between $\bar{U}$ and $\mathrm{R}{\mathrm{t}}_{90}$ at both depths. Consequently, the gas movement was enhanced by the wind in the fairly tilled soil. Furthermore, the decrease in both $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ with increasing $\bar{U}$ at 11.7 cm deep was smaller than that at 4.7 cm deep, indicating that the wind effect on gas movement decreased with depth. This result was consistent with that of Pourbakhtiar et al. (2017), who showed that ${\mathrm{D}}_{\mathrm{w}}$ decreased with depth.

In the poorly tilled soil, ${\mathrm{t}}_{50}$ and ${\mathrm{t}}_{90}$ were significantly decreased even under slight wind. At 4.7 cm deep, $\mathrm{R}{\mathrm{t}}_{50}$ gradually decreased with the increase in $\bar{U}$. However, $\mathrm{R}{\mathrm{t}}_{90}$ was no more than 0.3 under the wind speed of 1.2 m s⁻¹ and did not decrease with further increase in $\bar{U}$. At 11.7 cm deep, the $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ were also low even under the wind speed of 1.2 m s⁻¹, and not negatively correlated with $\bar{U}$. These results indicated that the gas exchange was enhanced by weak wind lower than 1.2 m s⁻¹, but the more increase in the wind speed did not affect the gas exchange in the poorly tilled soil.

Comparison between the fairly and poorly tilled soil on the evaluated $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ showed that wind induced the gas movement more in the poorly tilled soil than in the fairly tilled soil under the slow wind speed. However, in the fairly tilled soil, the effect was enhanced with the increase in the wind speed and finally became close to that in the poorly tilled soil at the wind speed around 2.0 m s⁻¹. The difference by the mean clod size is attributable to the air permeability of these soils (Table 3), which was indicated by Levintal, Dragila, and Weisbrod (2019). In the poorly tilled soil, the wind effect already reached a plateau under mild wind because the inter-aggregate pores allowed air turbulence propagation and pressure fluctuations. In contrast, in the fairly tilled soil, because the propagation of air turbulence was attenuated more by the resistance of the inter-aggregate pores, the effect probably depended on the amplitude of air turbulence determined by the wind speed.

3.2. The molecular gas diffusion coefficient in an empty column

Figure 7 shows the measured temporal change in oxygen concentration at depths of 4.7 and 11.7 cm in the empty column. The molecular gas diffusion coefficient in air (${\mathrm{D}}_{\mathrm{o}}$) at 20°C and the gas transfer coefficient on the upper boundary ($\mathrm{K}$) was determined to be 0.163 ± 0.003 cm² s⁻¹ (mean ± S. D.) and 0.084 ± 0.006 cm s⁻¹, respectively. Because the obtained ${\mathrm{D}}_{\mathrm{o}}$ was similar to 0.16 cm² s⁻¹ that reported by Marrero and Mason (1972), the obtained ${\mathrm{D}}_{\mathrm{o}}$ and $\mathrm{K}$ were used hereafter.

Figure 7. Temporal change in oxygen concentration measured in the laboratory and its optimum solution obtained using the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ) for the empty column (n = 3). The temporal changes in concentration for all replicates were plotted, while the average of the most optimum numerical solutions for each measurement was shown. Note that the measured data are shown every 30 s.

3.3. The molecular gas diffusion coefficient in soil

Figure 8 shows examples of temporal change in oxygen concentration at 4.7 and 11.7 cm deep measured in a laboratory and the optimized solution of the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ). Because these experiments were performed without wind, ${\mathrm{D}}_{\mathrm{a}}$ in Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) can be regarded as molecular diffusion coefficient D_m. The D_m values of the poorly tilled soil, fairly tilled soil, and Mikawa silica sand at 20°C were 0.038 ± 0.002, 0.037 ± 0.002, and 0.030 ± 0.002 cm² s⁻¹, respectively. Figure 9 shows the relationship between air-filled porosity and gas diffusivity (${\mathrm{D}}_{\mathrm{m}}/{\mathrm{D}}_{\mathrm{o}}$), obtained in the present study and by Hamamoto et al. (2009), who measured the ${\mathrm{D}}_{\mathrm{m}}$ of repacked Narita sand and Nishi Tokyo loam with different particle diameters using N₂ as the purging gas. Although the bulk density of Mikawa silica sand in our study (1.35 g cm⁻³) was similar to that of Narita sand in Hamamoto et al. (2009) (1.35–1.37 g cm⁻³), the gas diffusivity of the Mikawa silica sand in our study was smaller than those of Narita sand, which might be attributed to the apparent retardation by the water solubility of CO₂ (Appendix 2).

Figure 8. Examples of temporal change in oxygen concentration measured in the laboratory and its optimum solution obtained using the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ) for (a) poorly tilled soil, (b) fairly tilled soil, and (c) Mikawa silica sand (n = 3). The temporal changes in concentration for all replicates were plotted, while the average of the most optimum numerical solutions for each measurement was shown. Note that the measured data are shown every 60 s.

Figure 9. Comparison of gas diffusivity (${\mathrm{D}}_{\mathrm{m}}/{\mathrm{D}}_{\mathrm{o}}$) between our results and that of Hamamoto et al. (2009). This figure is a modified version of Figure 6a presented by Hamamoto et al. (2009), with our results added. They measured the gas diffusivity of ‘Narita’ sand and ‘Nishi-Tokyo’ loam with different particle diameters, indicated in parenthesis in millimeters.

3.4. Applicability of gas diffusion equation to wind-induced gas exchange

Figure (10, 11, 12) show examples of temporal changes in oxygen concentration and their optimum solutions based on the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ) obtained from in situ measurements for each soil. Figure 13 summarizes the RMSE value of the optimum solutions. In the Mikawa silica sand, because the RMSE was smaller than 0.012 cm³ cm⁻³ and the shapes of the solution curves were close to the temporal trends in measured oxygen concentration, it could be regarded that the gas diffusion equation successfully reproduced the measured temporal change in oxygen concentration even under wind. However, in the fairly tilled soil, although the RMSE at the wind speed of 1.0 m s⁻¹ was as small as 0.007 cm³ cm⁻³, it increased gradually with $\bar{U}$, and the shapes of the solution curves no longer expressed measured trends under the wind speed of 2.0 m s⁻¹ (Figure 11). In the poorly tilled soil, the RMSE was high regardless of the wind speed. The failure in adopting the diffusion equation to the poorly tilled soil was also obvious from the deviation between the solutions and measured plots at both monitoring locations (Figure 12).

Figure 10. Examples of temporal change in oxygen concentration measured at the field and its optimum solution obtained using the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ) with the Mikawa silica sand. Note that the measured data are shown every 120 s.

Figure 11. Examples of temporal change in oxygen concentration measured at the field and its optimum solution obtained using the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ) with the fairly tilled soil. Note that the measured data are shown every 60 s.

Figure 12. Examples of temporal change in oxygen concentration measured at the field and its optimum solution obtained using the gas diffusion equation (Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) ) with the poorly tilled soil. Note that the measured data are shown every 30 s.

Figure 13. Relationship between average wind speed ($\bar{U}$) and RMSE for each fitting.

Levintal, Dragila, and Weisbrod (2019) demonstrated that, using the gas diffusion (dispersion) equation, the R² between the measured and calculated temporal changes in gas concentration decreased as the wind speed increased or the air permeability increased. To solve this problem, they added an advection term to the diffusion equation to fit the experimental results. Their modified model successfully reproduced the trends, although they reported uncertainties regarding using the advection-diffusion equation from a physical perspective. Alternatively, in this study, the shapes of the temporal change in the oxygen concentration were different among the experimental runs (Figure (11, 12)). Considering this feature, a gusty mass flow might occur in the soil column during the in situ measurements, resulting in high RMSE. However, further discussion on the mechanisms cannot be derived from the present experiments.

Although the diffusion model did not accurately reproduce the observed behavior in the tilled soil columns, the relationship between $\bar{U}$ and the relative gas transfer coefficient (${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$) that minimized the RMSE is shown in Figure 14 as a reference. In the Mikawa silica sand, ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ was smaller than unity, and no significant relationship was detected between $\bar{U}$ and ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$. In the fairly tilled soil, ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ was larger than unity and increased gradually as $\bar{U}$ increased. Additionally, a positive relationship between $\bar{U}$ and ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ was observed. In the poorly tilled soil, ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ was larger than that in the fairly tilled soil under all wind speed conditions, and the difference increased with the wind speed, even though the R² for the correlation between $\bar{U}$ and ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ was relatively low in the poorly tilled soil.

Figure 14. Relationship between average wind speed ($\bar{U}$) and the ratio of the apparent gas diffusion coefficient (${\mathrm{D}}_{\mathrm{a}}$) to the molecular gas diffusion coefficient (${\mathrm{D}}_{\mathrm{m}}$).

As shown above, the diffusion/dispersion equation hardly reproduces the gas movement through the soil layer with large clods under the moderate wind. Thus, the wind-induced gas transfer should be primarily quantified by the parameters that do not assume any models. However, rough estimates of the gas movement through the poorly fragmented soil layer are necessary for practical purposes in agriculture or environmental sciences. ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ shown in Figure 14 is considered useful to understand the range of the effect of wind on gas transfer in poorly fragmented soil that is often found in paddy fields.

4. Conclusion

This study quantified the effect of wind on gas transport in the clayey paddy soil layer comprised large clods based on in situ and laboratory experiments. Gas transfer through the paddy soil layers, composed of a few centimeters of clods, under natural wind was up to eleven times as quick as under calm conditions. The wind-induced gas exchange remained at maximum at a wind speed of more than 1.2 m s⁻¹ at 20 cm above the soil surface, with a mean clod size of 3.4 cm. In contrast, in the soil layer with a mean clod size of 1.9 cm, the effect of wind on gas exchange gradually increased with wind speed and finally became close to that in the poorly tilled soil at a wind speed around 2.0 m s⁻¹. The applicability of the gas diffusion equation deteriorated when the mean clod size changed from 1.9 to 3.4 cm, or the wind speed increased from 1.2 to 2.6 m s⁻¹. From these findings, the effect of wind should be considered in the analysis of the in situ gas exchange in paddy soil with large aggregates having a mean size larger than 2 cm. In such cases, we should note that the diffusion/dispersion equation cannot reproduce the behavior accurately.

Acknowledgments

We are grateful to the field management staff at the National Agricultural Research Center (NARO) for their experimental assistance and technical advice, Dr Katsuhiro Suzuki at NARO for providing us with the experimental field, and Dr Tatsuo Hosono at NARO for providing us with the meteorological data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JSPS (Japanese Society for the Promotion of Science) KAKENHI [20J14362].

Appendix 1:

Estimation of the range of the error and time lag of the measured O₂ concentration caused by the distance from the column to the sensors

The expected time lag due to the distance between the column and the sensor probe was analyzed based on the numerical solution of the diffusion equation. Because the tubes having an inner diameter of 0.5 cm and the length of 2 cm to connect the inner wall of the column and sensors allowed free interdiffusion of CO₂ and air, the O₂ concentration ($\mathrm{C}$) within the connecting tube follows:

(A1) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}={\mathrm{D}}_{\mathrm{o}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{x}}^2}$(A1)

(A2) $\mathrm{C}=\mathrm{g}(\mathrm{t})(x=0,\mathrm{t}>0)$(A2)

(A3) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{x}}=0(x=\mathrm{L},\mathrm{t}>0)$(A3)

(A4) $\mathrm{C}=0(0\le x\le \mathrm{L},\mathrm{t}=0)$(A4)

where $\mathrm{x}$ is the distance from the column (cm), $\mathrm{L}$ is distance from the column to the O₂ sensor probe (=2 cm), and $\mathrm{g}(\mathrm{t})$ denotes the temporal O₂ concentration in the column at the depth of the O₂ sensor (cm³ cm⁻³). Generally, $\mathrm{g}(\mathrm{t})$ is also influenced by the diffusion to the sensor. However, we ignored it because the horizontal diffusion into the sensors were small compared to the vertical diffusion in the column. $\mathrm{g}(\mathrm{t})$ was calculated by solving the boundary problem described by equations (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) , (5(5) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{z}}=0(\mathrm{z}=12.6,\mathrm{t}>0)$(5) ), (6(6) $\mathrm{C}=0(0\le \mathrm{z}\le 12.6,\mathrm{t}=0)$(6) ), and (7(7) $\mathrm{C}=0.21(\mathrm{z}=0,\mathrm{t}>0)$(7) ). To estimate the time lags between the O₂ concentration in the column and the measured ones by the sensors, ${\mathrm{D}}_{\mathrm{a}}/\mathrm{a}$ ranging from 0.060 to 0.620 cm² s⁻¹ was applied for calculating $\mathrm{g}(\mathrm{t})$. Note that the obtained ${\mathrm{D}}_{\mathrm{a}}/\mathrm{a}$ in this study was within this range. Fig. A1 shows the evaluated difference in O₂ concentration in the column and at the sensor probe for the cases assuming ${\mathrm{D}}_{\mathrm{a}}/\mathrm{a}=0.620\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}\mathrm{a}\mathrm{n}\mathrm{d}0.060\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}$, as examples. Although the maximum difference in the concentration was expected in the rapid increasing stage and cases, the time lags almost fell within 13 ± 1.5 s regardless of the elapsed time and ${\mathrm{D}}_{\mathrm{a}}/\mathrm{a}$ in the column.

Figure A1. Comparison between the oxygen concentration in the column and at the sensors after the numerical simulation. (a) ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{a}}_{}=0.620\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}$ (b) ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{a}}_{}=0.060\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}$. The time lags are represented by the distance between the short vertical bars.

Appendix 2:

On the influence of dissolution of CO₂ in the soil moisture

Because the solubilityof carbon dioxide in water is so high, the injected CO₂ gas probably dissolved to the moisture in the soil aggregates. Assuming the concentration of CO₂ in the gas and liquid phases is in equilibrium following Henry's law, the volumetric concentration of CO₂ in both phases can be simply modeled as:

(A5) ${\mathrm{C}}^{\mathrm{C}{\mathrm{O}}_2}={\mathrm{K}}_{\mathrm{H}}{\mathrm{C}}_{\mathrm{l}}^{\mathrm{C}{\mathrm{O}}_2}$(A5)

where ${\mathrm{C}}^{\mathrm{C}{\mathrm{O}}_2}$ is the CO₂ concentration in the gas phase (cm³ cm⁻³), ${\mathrm{C}}_{\mathrm{l}}^{\mathrm{C}{\mathrm{O}}_2}$ is the CO₂ concentration in the liquid phase (cm³ cm⁻³), and ${\mathrm{K}}_{\mathrm{H}}$ is the Henry’s coefficient (=1.14 after Fujikawa and Miyazaki 2005). If the gas movement in the soil can be represented by the diffusion equation, the CO₂ concentration obeys the following equation:

(A6) $\frac{\mathrm{\partial }(\mathrm{a}{\mathrm{C}}^{\mathrm{C}{\mathrm{O}}_2}{+\theta \mathrm{C}}_{\mathrm{l}}^{\mathrm{C}{\mathrm{O}}_2})}{\mathrm{\partial }\mathrm{t}}={\mathrm{D}}_{\mathrm{a}}\frac{{\mathrm{\partial }}^2{\mathrm{C}}^{\mathrm{C}{\mathrm{O}}_2}}{\mathrm{\partial }{\mathrm{z}}^2}$(A6)

where $\theta$ is the volumetric water content. Substituting Equation (A5) into Equation (A6) yields..

(A7) $(\mathrm{a}+\theta /{\mathrm{K}}_{\mathrm{H}})\frac{\mathrm{\partial }{\mathrm{C}}^{\mathrm{C}{\mathrm{O}}_2}}{\mathrm{\partial }\mathrm{t}}={\mathrm{D}}_{\mathrm{a}}\frac{{\mathrm{\partial }}^2{\mathrm{C}}^{\mathrm{C}{\mathrm{O}}_2}}{\mathrm{\partial }{\mathrm{z}}^2}$(A7)

Because the sum of the concentration of CO₂ and air is one and the proportion of oxygen in the atmosphere is constant, (A7) can be also represented as..

(A8) $(\mathrm{a}+\theta /{\mathrm{K}}_{\mathrm{H}})\frac{\mathrm{\partial }{\mathrm{C}}^{{\mathrm{O}}_2}}{\mathrm{\partial }\mathrm{t}}={\mathrm{D}}_{\mathrm{a}}\frac{{\mathrm{\partial }}^2{\mathrm{C}}^{{\mathrm{O}}_2}}{\mathrm{\partial }{\mathrm{z}}^2}$(A8)

where ${\mathrm{C}}^{{\mathrm{O}}_2}$ is the oxygen concentration in the gas phase (cm³ cm⁻³).

By comparing with Equation (2)(2) $\frac{\mathrm{\partial }\mathrm{C}}{\mathrm{\partial }\mathrm{t}}=\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathrm{a}}\frac{{\mathrm{\partial }}^2\mathrm{C}}{\mathrm{\partial }{\mathrm{z}}^2}$(2) , Equation (A8) shows that the elution of CO₂ from the soil aggregates delays O₂ exchange by a factor of $\mathrm{a}/(\mathrm{a}+\theta /{\mathrm{K}}_{\mathrm{H}})$, which does not depend on ${\mathrm{D}}_{\mathrm{a}}$. The factor $\mathrm{a}/(\mathrm{a}+\theta /{\mathrm{K}}_{\mathrm{H}})$ ranges from 0.63 to 0.68, 0.68 to 0.73, and 0.78 to 0.89 for the poorly tilled soil, fairly tilled soil, and Mikawa silica sand, respectively. These values were calculated from the actual water content and air-filled porosity in the columns provided as Table 1. Therefore, although the effect of dissolution of CO₂ cannot be ignored in the estimation of the diffusion coefficient itself, the relative diffusion coefficient ${\mathrm{D}}_{\mathrm{a}}/{\mathrm{D}}_{\mathrm{m}}$ or the relative gas transfer parameters $\mathrm{R}{\mathrm{t}}_{50}$ and $\mathrm{R}{\mathrm{t}}_{90}$ are not affected by the dissolution of CO₂.