Effect of Soil Volumetric Water Content on the CO₂ Diffusion Coefficient

Abstract

Purpose: The soil air diffusion coefficient (D_s) is particularly important for the study of soil gas diffusion movement, and there are still many uncertainties in the widely used methods; as such, a method was designed to in situ measure the soil gas diffusion coefficient. Methods: Four different soil media were selected and studied by means of a designed in situ measurement of soil gas diffusion coefficients, and these were compared and analyzed with the predictions of several commonly used prediction models. In addition, they were combined with gas transport models to validate the results of the empirical models that were obtained by the in situ measurements. Results: The results of the data indicate that increasing the volumetric soil moisture content decreases the soil gas diffusion coefficient, with changes in the soil gas diffusion coefficient for the small-grained quartz sand medium being similar to those predicted by the Buckingham model. The soil gas diffusion coefficients for the large-grained quartz sand were similar to the Millington and Quirk model predictions at low humidity; for increased humidity, it was instead similar to the Buckingham model predictions. The soil gas diffusion coefficients of the two active media were closer to those of the SWLR model with high C_m. In addition, the R² of the measured data was verified, by empirical modeling, to be greater than 0.54, and inversion experiments were conducted to verify that the results were consistent with those of the SWLR model. Conclusion: When measuring relative diffusion coefficients in the field, we recommend the in situ measurement method, which is more reflective of the actual situation in natural environments and provides more accurate data support for soil carbon flux studies.

1. Introduction

The carbon cycle refers to the exchange of carbon elements between the Earth’s biosphere, lithosphere, hydrosphere, and atmosphere, and its continuous circulation with the Earth’s movement. Soil respiration, as a key link in the global carbon cycle, has a profound impact on global carbon balance through its dynamics [1,2,3]. To assess the rate of CO₂ gas transport in soils, soil–air exchange becomes a key factor. Soil–air exchange occurs mainly through interconnected aerated pores in the soil, with diffusive gas movement being the main exchange mechanism [4]. The rate of gas diffusion in the soil is influenced by the soil gas diffusion coefficient (D_s), which is its main influence [5]. The soil gas diffusion coefficient is important for characterizing soil structure and pore space [6,7], and it is also a key parameter for studying gas transport processes [8]. Environmental factors such as temperature and humidity can affect the ability of air to diffuse into the soil [9,10]. The soil gas diffusion coefficient, as the most important driving parameter affecting CO₂ gas diffusion, can interfere with the use of measurement devices in extensive studies of soil respiration and CO₂ emissions from the soil surface. At the same time, this coefficient is a key parameter in the diffusion equation for continuous gas flux studies. Accurate measurements of the soil gas diffusion coefficient are therefore essential.

In the past decade or so, soil respiration and soil surface CO₂ efflux have been extensively studied, while research on the spatial and temporal variability and drivers of carbon efflux is ongoing [11]. The diffusion coefficient D_s (m²s⁻¹), which is a key parameter in these studies, is still being developed and researched for the measurement of new methods. To gain a more accurate understanding of the soil gas diffusion coefficient and to quantify changes in outflow during soil respiration [12,13], commonly used measurement methods currently include laboratory measurement methods and model estimation methods.

Laboratory measurement methods usually require the target soil to be brought to the laboratory for measurements [14,15]; this can disrupt the pore structure within the soil and make the measurement process relatively complex [16]. Furthermore, the spatial heterogeneity of the soil may lead to imprecise measurement data [17]. In recent years, the development of new sensors and measurement devices has led to a wider application of gradient-based methods in continuous gas flux studies [12,13,18,19,20,21,22]. However, these applications may be influenced by environmental factors [23], resulting in inaccurately measured and extrapolated relative diffusion coefficients (D_s/D₀) that are inaccurate and which produce large biases [16]. Model estimation methods are mainly based on linear or power function empirical and semi-empirical models of aerated porosity to calculate the soil gas diffusion coefficients; however, the applicability of different models may vary [24]. If these models are applied directly to estimate the relative diffusion coefficients without calibration and by using actual measurement data, this may lead to large errors [25]. Overall, some of the current methods for measuring soil gas diffusion coefficients are subject to environmental or experimental manipulation, which leads to problems in breaking the pore structure within the soil and to imprecise measurement results.

Therefore, in order to calculate the soil air diffusion coefficient more accurately, this paper combines the LI-COR8100 measured data to design a method to measure the soil air diffusion coefficient in situ, and to assess the accuracy and applicability of the calculation results of several models in soils with different humidities. An empirical model of soil volumetric water content and soil air diffusion coefficients is further constructed, which can respond to the relationship between soil volumetric water content and soil air diffusion coefficient in real time. Furthermore, at the same time (in order to validate the accuracy of the empirical model), a model inversion was carried out. By comparing and analyzing the results of the model inversion and the results of the measured data, we can provide effective suggestions for the calculation of the relative diffusion coefficient model in order to provide more accurate data and methods in future research.

2. Materials and Methods

2.1. Introduction to the Location

This study was conducted at Zhejiang A&F University, which is located in Hangzhou, Zhejiang Province, China (30°15′ N–30°16′ N, 119°43′ E–119°44′ E). The experimental site was located on campus in a maple park at an altitude of 60–70 m, covering an area of approximately 22,000 m². The park is mainly planted with Acer cinnamomifolium, Acer yangjuechi (Fang and Chiu), Acer palmatum Thunb., and Osmanthus fragrans (Thunb.) Lour. To create a wind-free environment, tents were used to shield the study area from near-surface winds. The research trials were conducted in autumn and winter, during which the average temperature was 9.5 ± 0.5 °C. The soil temperature at the time of the experiment was 13.5 ± 2 °C. By conducting the study in this specific environment, we aimed to investigate the effect of soil moisture on soil gas diffusion coefficients when external environmental factors were excluded; in addition, we aimed to provide an empirical basis for subsequent studies.

2.2. Experimental Materials and Calculation of Relevant Variables

A square sample area of 200 cm × 200 cm was selected in the maple garden, and experiments were conducted in the four corners of the sample area. Four deep cylindrical pits with a diameter of 50 cm and a depth of 50 cm were dug in the four corners, and each of the four experimental soil media were placed in the pits two months in advance. Subsequently, CO₂ concentration sensors (GMP 252, Vaisala Corporation, Helsinki, Finland), and temperature and humidity probes (JXBS-3001-TR, Weihai Jingxun Changtong Electronic Technology Co. (Weihai, China)) were installed. The CO₂ concentration sensor sampled once per second, and the data were stored on a computer. The sensors were buried at depths of 5, 15, and 25 cm below the soil surface, and they were used to measure the CO₂ concentration in the target soil, as well as the temperature and relative humidity of the soil. As the nearest woods were more than 300 cm away from the sensors, the effect of tree root respiration on the soil CO₂ measurements was negligible. Considering that the test area was cleared of annual grasses prior to the test, it can be assumed that CO₂ mainly came from the transfer that occurred from deep in the soil and from the production of active substances in the medium. In addition, we inserted, to a depth of 5 cm, the collar required for the Li-8100 convenient soil carbon flux measurement system (Li-Cor Bioscience Company, Lincoln, NE, USA) into the soil. The system was installed and tested in September 2022 and data collection began in November 2022 (Figure 1).

To avoid the potential impact of soil disturbance on soil CO₂ measurements, only the data collected after 20 November 2022 were included in the analysis. During the experiment, soil moisture was increased by watering and the data returned from both sensors were recorded, as well as the target soil data recorded with the Li-8100. Five soil samples were collected using a volumetric ring knife at different depths (0–3 cm, 3–6 cm, 6–9 cm, 9–12 cm, 12–15 cm) and these were returned to the laboratory for basic property measurement calculations. Four media were used in the experiment.

Table 1. Soil media physical properties.

Soil Medium	Particle Size * dmid/mm	Grain Size * dmax/mm	Volumetric Weight (Dry) g/cm3	Soil Particle Density g/cm3	Total Porosity Φcm3/cm3
Small grains of quartz sand	0.5	1	1.371	2.71	0.495
Large grains of quartz sand	1	2	1.375	2.63	0.478
Sandy soil	\	\	1.327	2.75	0.517
Loamy soil	\	\	1.358	2.8	0.515

* The particle sizes, both min. and max., are the minimum and maximum particle diameters of the media, respectively.

shows the physical properties of the soil media used in this study.

2.3. Relative Diffusion Coefficients (D_s/D₀)

The relative diffusion coefficient (D_s/D₀) was determined from the CO₂ gas diffusion coefficient in the soil (D_s) and the CO₂ diffusion coefficient in the air (D₀), where the CO₂ diffusion coefficient in the air (D₀) can be obtained from the semi-empirical equation proposed by Gilliland’s empirical formula:

$$D_0=\frac{435.7T^{3/2}}{P{\left(V_A^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+V_B^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2}\sqrt{\frac{1}{{\mu }_A}+\frac{1}{{\mu }_B}}$$

(1)

where T (K) represents the air temperature; P (Pa) represents the total pressure; μ_A and μ_B represent the molecular weight of gases A and B; and V_A and V_B (cm³/gmol) represent the liquid gram molar volume of gases A and B at their normal boiling point.

At a standard atmospheric pressure of P_s = 101 kPa and T = 273.15 K, the molecular diffusion coefficient of the CO₂ molecular diffusion coefficient in air is 0.138 cm²/s. The temperature used in this study was maintained at 5 °C. Therefore, D₀ requires a temperature correction based on the following equation:

$${D^{\prime }}_0(T_2)=D_0(T_1){(\frac{T_2}{T_1})}^{1.72}$$

(2)

where D₀′ (cm²/s) represents the diffusion coefficient of the corrected CO₂ in the air; T₁ (°C) represents 273.15 K, which is 0 °C; and T₂ is the temperature at the time of the experiment.

2.4. Introduction to Common Estimation Models

Buckingham presents the ratio of the D_s ratio to the diffusion coefficient of this gas in a free atmosphere; D₀ (D_s/D₀) is proportional to the square of the aerated porosity of the soil ε [26]. Penman, on the other hand, found in his experiments that when ε was between 0 and 0.7 cm³/cm³, the relationship between D_s/D₀ had a good linear relationship with ε [27]. Millington and Quirk proposed a model for estimating gas diffusion coefficients that considered total soil pore space [28]. Troeh et al. proposed an empirical formula based on existing models for a variety of soil texture types [29]. Moldrup et al. improved the model by taking into account the moisture characteristic curve and the bending coefficient. Moldrup et al. based their model on that of Millington and Quirk, whereby they took into account the reduced term for the increase in pore curvature due to moisture entry [30]. The SWLR (structure-dependent water-induced linear reduction) model was developed by Moldrup et al., and it works by adding the porous media complexity factor C_m to the diffusion coefficient model; moreover, the model takes into account the different soil structures and retains the water-induced linear reduction term.

1.

Buckingham model [26];

$$\frac{D_s}{D_0}={\epsilon }^2$$

(3)

2.

Millington and Quirk models [28];

$$\frac{D_s}{D_0}=\frac{{\epsilon }^{\raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{{\varphi }^2}$$

(4)

3.

SWLR model [30].

$$\frac{D_s}{D_0}={\epsilon }^{(1+C_m\cdot \varphi )}\frac{\epsilon }{\varphi }$$

(5)

where C_m represents the porous media complexity factor in the model for air-dry filled soils and C_m = 1; for the in situ soils, C_m = 2.1; Φ (cm³/cm³) is the total soil porosity; and ε (cm³/cm³) is the aerated porosity ε.

$$\varphi =1-\frac{{\rho }_b}{{\rho }_s}$$

(6)

where ρ_b (g/cm³) represents the experimental soil volumetric weight and ρ_s represents (g/cm³) the particle density of the soil.

$$\epsilon =1-\frac{{\rho }_b}{{\rho }_s}-{\theta }_v$$

(7)

where θ_v (cm³/cm³) represents the volumetric water content of the soil, whereas D_s/D₀ represents the ratio of the directly measured diffusion coefficient of the soil gas to the diffusion coefficient of the gas in the free atmosphere (when at the same temperature and atmospheric pressure).

2.5. Method for Determining and Calculating the Effective Soil Gas Diffusion Coefficient

The experimental design of this paper uses the LI-cor 8100 instrument to measure the effective CO₂ gas diffusion coefficient of the soil in the field.

Using the data recorded by the LI-cor8100 instrument, the first law of FICK can be used to calculate the soil CO₂ gas diffusion coefficient, D, which is measured with the LI-cor 8100 instrument:

$$F=-D_s\frac{dC}{dz}$$

(8)

where F (μmol m⁻²/s) denotes the flux of CO₂ at the soil surface; C (μ mol m⁻³) denotes the CO₂ concentration in the soil measured by the CO₂ concentration sensor, converted from ppm; and Z (cm) denotes the distance between the CO₂ concentration sensor and the 8100.

At the beginning of the experiment, we placed the 8100 device on a preset iron ring which was inserted into the soil at a depth of 5 cm and recorded simultaneously. According to previous studies [31], it has been established that gas transport in soil occurs mainly by diffusion. In this study, we assumed that the soil was isotropic and used real-time monitoring methods to obtain the field soil data.

2.6. Gas Transport Model Validation Inverse Generation

During the experimental period, the before and after changes in the soil CO₂ gas source term in the sample area were relatively small and negligible; such that, according to the one-dimensional model of gas transport in soil (Fick’s second law), it follows that

$$\theta \frac{\partial C}{\partial t}=D_{tot}\frac{{\partial }^{2}C}{\partial Z^2}$$

(9)

where θ (cm³/cm³) indicates the effective porosity of the gas; C (μmol m⁻³) denotes the CO₂ concentration in the soil measured by the CO₂ concentration sensor, converted from ppm; t (s) denotes time; D_tot (cm²/s) denotes the effective diffusion coefficient of the gas in the soil for CO₂; and Z (cm) indicates soil depth.

Our method of using FICK’s second law is to use the data collected by the CO₂ concentration sensors at 5 cm and 25 cm as boundary conditions, using the first measurement as the initial condition, and using the numerical solution for the calculation.

In the absence of environmental perturbations, the transport model D_tot is equal to D_s. When the volumetric soil water content changes, i.e., when the environmental factors change significantly, their D_tot changes to

$$D_{tot}=D_s+{D^{\prime }}_s$$

(10)

where D_s (cm²/s) represents the apparent diffusion coefficient of CO₂ in the soil, and D_s′ (cm²/s) denotes the enhanced diffusion coefficient of CO₂ in soil, which can be caused by environmental changes.

2.7. Data Analysis

Field measurements were saved and pre-processed using Microsoft Excel (Office 365), followed by Origin (Origin Lab, 2019b, Northampton, PA, USA), and MATLAB (MathWorks, r2020b, Natick, MA, USA) for data analysis and the computation of the empirical models, respectively.

3. Results and Discussion

3.1. Soil Moisture and CO₂ Flux Changes

Figure 2 shows the values of the CO₂ fluxes with soil volumetric water content for different types of media in the experiment. As shown in the figure below, the fluxes of all four media decreased with increasing soil moisture. In particular, the CO₂ flux decreased the fastest when the soil volumetric moisture content reached 7%. Simultaneously, the volumetric soil moisture content of the coarse sands reaches the maximum water-holding capacity of this type of soil in its natural environment when it reaches 8%. Beyond this level, the volumetric water content of the soil decreased rapidly and returned to 8%, which was not the case for the other three soil media.

Overall, as the humidity increased, the CO₂ fluxes first decreased slowly, and when the humidity reached a specific value, the CO₂ fluxes stabilized when the humidity reached a specific value. Each measurement showed a small increase in flux owing to a slight decrease in soil moisture over the course of the experiment.

In the experiments with both sandy and loamy soils, we found that both media showed a steady state with the small changes in flux at the beginning of the moisture increase. When the humidity increased to a certain level, the same steady state occurred. However, in the experiments with the two-quartz sand media, the CO₂ fluxes exhibited a substantial decrease at a certain humidity.

3.2. Soil Moisture and Soil CO₂ Concentration in the Soil

At the same time, we also observed how the CO₂ concentration interacted with the soil volumetric water content. As the two sandy soils did not contain reactive material with increasing volumetric soil water content in Figure 3, the CO₂ concentrations showed a decreasing trend in both the sandy and loamy soils. However, both the sandy and loamy soils contained active substances; thus, when the volumetric soil water content started to increase, these active substances were stimulated, leading to an increase in the CO₂ concentrations [5,32]. However, as the volumetric water content of the soil increased to a certain range, the CO₂ concentration also ceased to increase and showed a gradual stabilization that was similar to that of sandy soils. During the experiment, the initial volumetric water content of the sandy soil was lower than that of the loamy soil, and the sensitivity of the intrinsically active substances to the moisture was more pronounced. Therefore, at the stage when the moisture content started to rise as the active matter within the sandy soil was stimulated by the increased moisture content, a large amount of CO₂ at 5, 15, and 25 cm occurred, resulting in a rapid increase in CO₂ concentration. However, because the active matter content in the sandy soils was lower than that in the loamy soils, the CO₂ concentrations were lower in the sandy soils than in the loamy soils at the same moisture level. In addition, the CO₂ concentration values were lower in the sandy soils than in the loamy soils when they reached their maximum.

3.3. CO₂ Concentration Gradient Variation and CO₂ Flux Changes

According to FICK’s law, the variation in soil CO₂ fluxes is mainly affected by changes in diffusion coefficients and CO₂ concentration gradients. As shown in Figure 4, we can observe the relationship between the changes in CO₂ concentration gradients within several media and the fluxes. First, in the two different particle sizes of quartz sand media, the CO₂ concentration gradients remained relatively constant, whereas the fluxes showed a decreasing trend. However, in the two active soils, the CO₂ concentration gradients showed an increasing trend, whereas the CO₂ fluxes tended to plateau. These results reveal the relationship between CO₂ concentration gradients and fluxes.

3.4. Relative Diffusion Coefficients for Different Soils (D_s/D₀)

In CO₂ flux calculations, the soil air diffusion coefficient is of great importance because it affects the soil CO₂ flux values in real time. Owing to its greater porosity and better permeability than several other media, large-grained quartz sand has a 25 cm CO₂ concentration that is lower than that found in other media (as shown in Figure 3). As the volumetric water content of the soil is increased, the CO₂ concentrations decrease at the lowest rate with the smallest concentration differences. Sandy and loamy soils with good water absorption capacity and high water-holding capacity showed the lowest CO₂ concentration decreases, and the concentration differences were different from those of small-grained quartz sand. At the same time, the various media also showed a slight decrease in soil volumetric water content, resulting in a decrease in the CO₂ concentration. This may be due to evaporation or the infiltration of water diluting and carrying away part of the CO₂ from the soil, thus causing this phenomenon to occur.

Figure 5 shows the relative diffusion coefficients of the four different media measured by the real method (D_s/D₀) when compared with the three commonly used prediction models. The relative diffusion coefficients of all four media decreased with increasing moisture content under the effect of soil volumetric moisture content [33]. Figure 5a–d shows the relative diffusion coefficient values for the small-grained quartz sand, large-grained quartz sand, sandy soil, and loam, respectively, compared to the three commonly used prediction models.

(1)

The measured relative diffusion coefficients for the small grains of quartz sand were close to those predicted by the Buckingham model.

(2)

The measured relative diffusion coefficients for the large-grained quartz sand were closer to those predicted by the Millington and Quirk models at low volumetric water contents; however, as the volumetric water content increased, the values of the relative diffusion coefficients were closer to those predicted by the Buckingham model.

(3)

The measured relative diffusion coefficients for sandy and loamy soils were generally smaller than those estimated using the prediction models. This may be due to the fact that sandy and loamy soils hold water better, resulting in smaller values of the measured relative diffusion coefficients.

Owing to the different textures of the various soil media, the soil media also behave differently in terms of volumetric water content. Large-grained quartz sand has a weaker water-holding capacity in field experiments, whereas small-grained quartz sand has a better water-holding capacity than larger-grained quartz sand. Similarly, loamy soil and sandy soil have a better water-holding capacity than the two types of quartz sand; therefore, the relative diffusion coefficients obtained from the field measurements were smaller than those obtained from the predictive model.

We found that the SWLR model predictions were both over- and under-predicted, as shown in Figure 5. Therefore, we further explored the SWLR model.

In our study of the SWLR model, we found that in direct measurements of the dry-to-wet soil gas diffusion coefficient (D_s/D₀) data, the recommended range for C_m (porous media complexity factor) is 1–3 [27]. To compare the magnitude of the predicted diffusion coefficient with the measured diffusion coefficient, we explored the performance of the C_m in the recommended range.

Figure 6a shows that the actual measured relative diffusion coefficients for the small-grained quartz sand were not only close to the Buckingham model, but also better matched the predicted values of the SWLR model at C_m = 1.5. The actual measured relative diffusion coefficients for the large-grained quartz sand were in close agreement with the SWLR model predictions at C_m = 1 (Figure 6b). As humidity increased, the measured relative diffusion coefficients were similar to those predicted by the SWLR model at C_m = 1.5. Our analysis of the large-grained quartz sand for C_m may vary with increasing humidity.

The same phenomenon was observed in both the sandy and loamy soils (Figure 6c,d). The relative diffusion coefficients obtained from the actual measurements in both media were compared with the SWLR model. When the value of C_m was 3, the results obtained by the prediction model were closer to the actual measurements.

In the presence of water in the soil pore space, gases diffuse through the interconnected aerated pores. Based on the measured data, we analyzed the relationship between the relative diffusion coefficients of gases in small-grained quartz sands, sandy soils, and loamy soils at different soil volume water contents and made some recommendations (Figure 7). We did not provide an empirical model for large-grained quartz sands because of their weak water-holding capacity and because large-grained and large-pore-size soils are relatively rare in nature. It should be noted that these results only apply to a few media when under the conditions of this experiment. For other textured soils, there may be differences in the relative diffusion coefficients obtained from the measurements.

3.5. Validation of the Predictions from Empirical Models of Relative Porosity for Several Media

To verify the accuracy of our empirical model for several media obtained through calculations, we conducted a 4 h long validation experiment. The experiments were performed in the same manner as in the previous tests and a gas transport model was chosen to validate our empirical models. By comparing Figure 8, we found that the predicted concentrations of the three media at a depth of 15 cm were similar to the actual measurements. Small-grained quartz sand showed a decrease in concentration due to an increase in the volumetric water content of the soil. Both the sandy and loamy soils with active properties showed an increase in their internal active matter as the volumetric water content of the soil increased, leading to an increase in CO₂ concentration with increasing water content. The fluctuating trend in the inversion of the diffusion coefficients was consistent with the actual measurements, and the change in concentration was similar to the actual measurements.

In particular, the small-grained quartz sand medium produced the best results, which was in general agreement with the actual measurements. Although the simulations of the active sand and loamy soil were not as accurate as those of the small-grained quartz sand, the difference was not significant—most likely because of the influence of the activity factors in these two active media.

4. Discussion

There was a close relationship between the soil moisture and soil gas emissions. When the volumetric soil water content changed, it affected the CO₂ concentration within the soil. In addition, the volumetric soil water content also affected the relative diffusion coefficient of the soil medium, which is in line with the findings of many researchers [34]. In studying the relative diffusion coefficients of soils, we found that volumetric soil water content has different effects in soils with different media. In areas with low soil activity and poor soil quality, the rate of soil discharge decreases if it is affected by rainfall. In contrast, in areas with fertile soils and abundant rainfall, rainfall may increase soil activity in the initial stages [32], with the rate of soil carbon emissions gradually stabilizing as rainfall increases [5,34].

From the field measurements, we found that as the volumetric water content of the soil increased, the internal soil CO₂ concentration partially dissolved in the water and decreased slightly as the water evaporated. In addition, the number of reactive factors within the soil affected the amount of internal soil CO₂, with natural soils having a greater increase by a large amount in their CO₂ concentration increases [30].

We further found that the commonly used prediction models require validation by subsequent experiments and differ somewhat from the relative diffusion coefficients measured in the field. Among the common prediction models, the Buckingham and Millington and Quirk models are more suitable for inactive and sandy environments [5]. The predicted values of the SWLR model are closely related to the porous media complexity factor, which is represented by C_m in their equations. The C_m value is lower in soil media that are simple in composition and easy to analyze. We also found that the C_m values for large-grained quartz sands were lower in low-water-content environments, but were increased with increasing moisture content. In practice, the complexity factor of porous media may also increase with increasing humidity during measurement. Therefore, we recommend the use of field–field measurements when calculating the relative diffusion coefficient in the field.

In practice, the moisture content of sandy soil is difficult to determine in laboratory measurements, where the aerated porosity ε is particularly small. The volumetric soil water content may be influenced by the water-holding capacity of the medium, which in turn affects the internal soil CO₂ concentration within the soil. Therefore, objective laws of nature must be followed when predicting the relative diffusion coefficient of the medium.

When measuring soil carbon fluxes in the field in the event of sudden rainfall, this can affect the results of soil carbon flux measurements because of the inability of rainwater to enter the confined air chamber [22], which in turn affects the prediction of carbon flux emissions in the region. In this study, the relative diffusion coefficients of only the two quartz sands and the two common soil media were measured, thus there were limitations to the prediction model results. A number of countermeasures were taken to exclude external environmental factors. However, in natural environments, these factors often occur simultaneously. Therefore, in future experiments, we can target characteristic soils and analyze multiple environmental factors simultaneously in a field environment.

In conclusion, understanding the relationship between soil moisture and soil gas emissions is important for predicting carbon flux in different soil types. The application of predictive models requires the consideration of a variety of factors in the natural environment, as well as the effect of soil volumetric water content on soil carbon fluxes. Through field measurements and model validation, we could predict soil carbon fluxes more accurately and provide strong support for future research on environmental protection and climate change.

5. Conclusions

We designed a method for measuring soil gas diffusion coefficients in situ by the changes in the relative diffusion coefficients (which are calculated by increasing volumetric soil water content), by calculating the change in relative diffusion coefficients, and by validating the experimental results with a gas transport model. The following conclusions were drawn:

(1)

An increase in the volumetric water content of the soil in the experimental medium decreases the aerated porosity ε of the medium, which in turn decreases the relative diffusion coefficient of the medium. However, in reactive sand and loam media, the increase in volumetric water content firstly increases the internal CO₂ concentration, which in turn increases the concentration gradient (but this is not the case for inactive quartz sand media).

(2)

By comparison with several prediction models, it was found that the Buckingham model and the Millington and Quirk model were more effective in simple soil media. In complex soil media, the magnitude of the C_m value for the SWLR model affects the prediction accuracy of the model.

(3)

In order to better calculate the relationship between the soil volumetric water content and soil air diffusion coefficient, we constructed an empirical model composed of soil volumetric water content and the soil air diffusion coefficient. The accuracy of the empirical model was verified using another experiment and gas transport model. The results of our empirical model are essentially the same as those of the actual measurements.

Therefore, when measuring the relative diffusion coefficients in the field, we recommend this in situ measurement method. This method better reflects the actual situation in the natural environment and provides more accurate data support for soil carbon flux studies.