Effect of wind turbulence on monitoring soil CO2 flux using the closed gas chamber method

This study evaluated the performance of closed chamber monitoring of soil carbon dioxide (CO2) flux in a wind turbulence environment to improve the accuracy of constructing an ecosystem carbon budget. The effect of wind turbulence–induced barometric pressure fluctuations on soil CO2 emissions was explored using soil pore pressure difference data from different monitoring sites in the field, and the factors associated with errors in the monitoring of closed gas chambers were analysed. Subsequently, a gas chamber measurement error study was conducted in conjunction with the flux calculation model based on the phenomena observed in the field. The results showed that the simply designed closed gas chamber exerted a strong isolation effect on wind turbulence and did not simulate the actual monitoring environment. The error of the linear flux model in a turbulent wind environment for 10 min was 3%–7% greater than that in the absence of wind (error of 12%), and the calculation error of the exponential fitting model in a turbulent environment was also close to 10%. In addition, the error in the calculation model was positively correlated with the wind turbulence intensity and soil dispersion coefficient. Therefore, for a windy environment, the closed gas chamber and flux calculation models must be improved. Otherwise, a large deviation between the monitored flux and actual values will occur.


Introduction
Soil carbon dioxide (CO 2 ) gas emissions are a crucial component of the terrestrial carbon cycle. Globally, the estimated soil CO 2 released into the atmosphere is 98±12 Pg C (Bond-Lamberty and Thomson 2010), approximately 15 times the current annual amount released from fossil fuel burning (Denman et al 2007, Goffin et al 2015. Therefore, accurate measurement of the flux of stable micro gas (CO 2 ) from the Earth's surface is important for assessing the global carbon revenue and greenhouse effects caused by greenhouse gases (Abbasi et al 2021, Forde et al 2019, Knorr et al 2005, Sahoo and Mayya 2010, Sanz-Cobena et al 2021 and provides important data for the implementation of carbon balancing programmes.
In the past few decades, there has been an increase in the number of soil CO 2 flux monitoring technology, from alkali solution absorption to chromatography, box law, and micro gas simultaneous methods; however, the current monitoring technology primarily used is based on air chambers. This method is widely used in carbon cycling and other environment-related studies (Norman et al 1997, Davidson et al 2002, Xu et al 2006, Sahoo and Mayya 2010, Jacinthe 2015, Poblador et al 2017, Buragiene et al 2019, Rittl et al 2020, Zhang et al 2022. The gas chamber used for monitoring soil CO 2 flux is divided into a closed chamber system (also known as a transient or unstable system) and an open chamber system (also known as a steady-state system) (Livingston and Hutchinson 1995, Davidson et al 2002, Xu et al 2006. The measurement principle of the closed gas chamber was based on the data obtained from CO 2 concentration in the chamber and the corresponding model for the soil CO 2 flux calculation. These chambers generally have a short monitoring time, are easy to use. (e.g. Li-6400-09 and Li-8100 of the Li-COR Bioscience Company in Lincoln, Nebraska; SRC-1 of PP systems, Hertfordshire, UK; SRS-1000 of ADC in Holdstone, UK). The basic principle of the open-air chamber is to extract gas from the chamber and pump the gas from the environment into the chamber, which then continues in a cycle. After the CO 2 concentration in the gas chamber reaches a steady state, the CO 2 flux is calculated using the gas flow rate and the CO 2 concentration at the inlet and outlet of the gas chamber. The use of open-air chambers requires further research (Fang and Moncrieff 1998, Butnor et al 2003, Edwards and Riggs 2003, Subke et al 2003, Xu et al 2006. Currently, commercial monitoring chambers are also in use (e.g. SRC-mv5 soil CO 2 flux chamber; Dynamax Inc., Houston, Texas, USA). However, currently the closed air chamber that dominates the market, requires the measurement to be done without air pressure fluctuations or wind, but the measurement process involves environmental air pressure fluctuations. Atmospheric pressure changes cause fluctuations in soil gases, increasing the rate of soil gas exchange, which is usually associated with barometric pressure changes of several hundred Pa over several hours (Clements and Wilkening 1974, Massmann and Farrier 1992, Sánchez-Cañete et al 2016, Levintal et al 2019. In addition, the exchange of gases between the soil and atmosphere is enhanced by the pressure difference generated by the surface wind or by the turbulent effect of the wind. This phenomenon is known as wind-induced transport, where pressure changes range from a few Pa to several tens of Pa within a few minutes. (Kimball and Lemon 1971, Takle et al 2004, Nachshon et al 2012, Sánchez-Cañete et al 2016, Pourbakhtiar et al 2017, Poulsen et al 2018, Levintal et al 2019. Changes in atmospheric pressure have a larger time scale for soil gas transport, whereas wind turbulence induces gas transport, which tends to have high frequencies and short-term characteristics. In short-term monitored closed air chambers, wind turbulence causes ground air pressure fluctuations to become one of the most important influencing factors. As the closed air chamber blocks the pressure pump effect or wind pump effect caused by atmospheric turbulence in the measurement, this attenuates the driver of atmospheric flow of the soil CO 2 , resulting in a deviation in soil CO 2 flux measurement. However, the perturbation of wind turbulence during actual field measurements is inevitable; therefore, this study evaluates the performance of closed air chamber used to measure the carbon flux in the wind environment and the design of the air chamber.
The enhancement effect of air pressure fluctuations on gas transport in porous media has been previously investigated (Maier et al 2012, Pourbakhtiar et al 2017, Levintal et al 2019 and the gas transport process was divided into three control states (figure 1) based on wind speed and soil permeability. However, the performance of a closed air chamber in a fluctuating pressure environment has not been studied. Furthermore, the underestimation effect of closed air chamber measurements has been studied. However, the computational model used in the closed air chamber and air chamber design were primarily analysed (Livingston and Hutchinson 1995, Gao and Yates 1998, Livingston et al 2006, Sahoo and Mayya 2010 but the actual environmental disturbance causing an error in the measurement value of the air chamber was not studied.
In this study, we determined the efficiency of the air chamber design by observing the soil pore pressure at different measurement points in the field and examined the shielding effect of the air chamber against wind turbulence in a turbulent wind environment in conjunction with the differential pressure values recorded by the sensors. We assessed, based on field measurement phenomena and mathematical modelling analysis, the bias in flux measurements of a closed air chamber when used in an environment where wind turbulence causes fluctuations in surface air pressure.

Method
To understand the bias in the measurements of confined air chambers owing to wind turbulence under natural conditions, we collected field measurement data and analysed them using a flux calculation model. First, we collected data on near-surface wind speed, soil pore pressure, and other factors that can generate errors in the field monitoring environment and explored the influence of air pressure fluctuations caused by wind turbulence on soil CO 2 gas emissions. Next, based on the phenomenon observed in the field-measured data combined with the closed flux calculation model, the relationship between wind turbulence and the closed air chamber monitoring the soil carbon flux was evaluated.

Field site description
Field data acquisition experiments were conducted in the autumn and winter of 2021. The collection point was located within the Maple Gardens of Zhejiang Agriculture and Forestry University (30°15′N 119°43′E, 60 m a.s. l). The garden plantings were primarily Acer cinnamomifolium, A. yangjuechi (Fang and Chiu), A. palmatum Thunb., and Koelreuteria paniculata Laxm., and the soil surface cover was primarily Festuca ovina Linn. The soil was clay loam (figure 2(a)), of which 0-8 cm was a humus layer and 10-30 cm was a deposition layer. The field experiment was divided into two parts: equipment deployment and data monitoring. To avoid any negative impact, we selected a flat land to deploy the equipment 1 month prior to commencement of the experiment. Two stainless-steel collars (inner diameter, 20 cm; height, 5 cm) and a polyvinyl chloride collar (inner diameter, 20 cm; height, 5 cm) were inserted into the soil and labelled 1, 2, and 3, respectively (figure 2(c)). The upper end of the collar was embedded in a stainless-steel capillary with (inner diameter, 8 mm; wall thickness, 1 mm; length, 130 mm). After completing the installation of the chamber collar base, 10 cm from the outer wall of the collar (on the side of the capillary), the soil layer was cut vertically at a depth of approximately 40 cm (figure 2(a)). Next, three stainless-steel capillaries (inner diameter, 8 mm; wall thickness, 1 mm; length, 200 mm) were inserted at depths of 10, 20, and 30 cm, and the other end was connected to a silicone tube ( figure 2(b)).  Schematic (b) of the deployment experimental equipment in the field. The scene map (c) after the experiment showing the location of each device; the three-dimensional anemometer is located in the southeast direction, 1 m from the ground, and the three collar bases are located in the northwest of the anemometer in a triangular layout, marked as Nos. 1, 2, and 3.

Data monitoring device
After the equipment was deployed for 1 month, the field experiment was completed when the wind speed was high on 18th November, 28th November, and 5th December, 2021. A differential pressure sensor (HCS3051, Qingdao Huacheng M&C Equipment Co., Ltd, China) was used to collect differential pressure data from different soil layers. The accuracy of the differential pressure sensor was 0.075%, accounting for 200 Pa. Before the experiment was performed, the differential pressure sensor was calibrated; the two ends of the sensor were inserted into the calibration system (Xu et al 2006, Mohr et al 2020, and the pressure difference value was recorded. Next, the high-pressure side (H) was connected to a silicone tube that was inserted 10, 20, and 30 cm from the soil surface according to the monitoring needs, and the low-pressure side (L) was connected to the stainless-steel capillary on the soil surface; data were logged at 1 s intervals ( figure 2(b)). Simultaneously, a threedimensional anemometer (EC-A3, Jinzhou sunshine Meteorological Technology Co., Ltd, China) was installed on flat ground 1 m from the ground next to the stainless-steel collar. Specific locations are shown in figure 2(c). The wind speed data were collected on-site in real time and logged at 1 s intervals. A cylindrical closed gas chamber (diameter, 20 cm; height, 12 cm) with a designed balanced differential pressure function and without a designed balanced differential pressure function was used for CO 2 flux monitoring, and an IRAG Infrared CO 2 Concentration Sensor (DCO 2 -TFW1, Beijing Dihui Technology Co., Ltd, China) was installed in the centre of the gas chamber (5 cm). The CO 2 concentration data were logged at 2 s intervals.

Gas transport model
According to the literature (Levintal et al 2019, Maier et al 2012, the gas transmission mechanism in the windinduced porous medium will be different for the gas permeability of different soils (figure 1). When the gas permeability or wind speed is greater than a certain value (Regime 3), gas transport is dominated by advection mechanisms. Gas transmission in porous media (soil) is typically described by the advection-diffusion equation (Hamamoto et al 2009, Pourbakhtiar et al 2017.
In Regime 2, the gas transport mode was dominated by the dispersion mechanism, that is, the vertical transport of air mass flow in the soil caused by the fluctuation of air pressure on the soil surface. With the alternation of pressure fluctuations, gas convection also alternates up and down; thus, the net vertical airflow into and out of the soil is zero (Maier et al 2012, Pourbakhtiar et al 2017. This implies that the movement of gas in porous media caused by pressure fluctuations because of wind turbulence can be regarded as a dispersion process, and the gas transport equation is as follows (Goffin et al 2015, Pourbakhtiar et al 2017: where D e [m 2 /s] is the effective diffusion coefficient (or 'apparent diffusion coefficient') of CO 2 in the soil medium, representing the sum of molecular diffusion and mechanical dispersion. The specific equation is as follows (Auer et al 1996, Bear 2013: where D S [m 2 /s] is the soil molecular diffusion coefficient, which can be estimated from the molecular diffusion coefficient (D 0 ) in air. Two well-known D s models are the King (1905) and Millington and Quirk (1961) is the effective porosity of the medium, and j [m 3 /m 3 ] is the total porosity of the medium. a n | | [m 2 /s] velocity-dependent dispersion term, which is velocity-dependent or mechanical dispersion. α is the dispersion, which reflects the complexity of pore space connectivity at the research scale. In uniform media, the value of α is very small. If there is no gas advection in the medium, the effective diffusion coefficient is the molecular diffusion coefficient D s . At this time, the gas transport mechanism becomes diffusion-dominated, that is, the Regime 1 phase (figure 1). However, in the case of pressure fluctuations, the net speed may be zero, but n | | is not zero, at which time D e > D s (Auer et al 1996).

Closed chamber monitoring model
According to the law of species mass conservation and the monitoring principle of the closed gas chamber, the model was established; that is, the mass of the gas emitted from the soil was equal to the mass of the gas accumulated in the gas chamber. Additionally, some assumptions were made to facilitate the model analysis: CO 2 gas mixing in the gas chamber is instantaneous and uniform at any time. The relationship equation is as follows: is the mass of CO 2 gas emitted by the soil, M a [g] is the mass of CO 2 gas accumulated in the gas chamber, V [m 3 ] is the volume of the gas chamber, C(0) [g/m 3 ] is the CO 2 concentration at the soil interface, A [m 2 ] is the contact area between the gas chamber and soil, t [s] is the measurement time, and f [g m −2 s −1 ] is the CO 2 gas flux. Thus, equation (4) can be rewritten as follows: This equation can then be solved using Laplace transform combined with equations (2) and (5).
where ¢ C 0 s 0 ( ) is the spatial derivative of the initial concentration of CO 2 in the soil when z=0 and q is defined as / qp D . e Subsequently, the inverse Laplace transform of equation (6) can be used to obtain the distribution function of CO 2 concentration in soil with space and time, and that combined with the gas flux expression at t=0, that is, Fick's first law, the distribution function of CO 2 gas concentration with time at z=0 can be obtained (see Livingston et al (2006) for detailed derivation steps).

Data analysis
The field-measured results were saved and pre-processed using Microsoft Excel 2020 and subsequently mapped and analysed using MATLAB (MathWorks, r2020b, Natick MA, USA). Mathematica 12 was used to construct the closed gas chamber monitoring model and conduct error analysis.

Result
3.1. Turbulence effect of wind Relevant data monitoring experiments were conducted when the wind speed had a significant effect on them. Notably, 1) the underground differential pressure vent pipe installed 1 month in advance was partially blocked (20 cm for position 1; 20, and 30 cm for position 3), and the data could not be collected as planned. To avoid a change in the planning of the experiment, the differential pressure (DP) at 10 cm was measured for research; 2) to analyse the turbulence effect of wind, 10 min of wind speed (1 m on the surface) and the differential pressure on the soil layer (10 cm above and below, no monitoring room) were randomly selected. The results are shown in figure 3. As shown in figure 3(a), the fluctuation range of the wind speed was relatively stable, total wind speed fluctuated between 0 and 1 m s −1 , and wind speed in the vertical direction was relatively evenly distributed between −1 and 1 m s −1 . The pressure difference between the soil pore surfaces (10 cm) is shown in figure 3(b). Its value fluctuates between −0.4-0.4 Pa, and the positive pressure ratio is slightly higher than the negative pressure ratio. The correlation between the surface wind speed and soil pore pressure difference is shown in figure 3, demonstrating a significant correlation between the vertical wind speed and pressure difference (R 2 =0.17, P<0.001). The main reason for this correlation is that the turbulence of the wind is the impetus of the fluctuation of the surface air pressure, which leads to a change in the air pressure in the soil (Levintal et al 2019).
3.2. Analysis of closed gas chamber monitoring 3.2.1. Gas chamber without the design of an equilibrium pressure function The data in figure 4 show the variation in the differential pressure on the soil layer when the total wind speed fluctuates significantly (in the range of 0∼3 m s −1 ). This phenomenon will increase the effective diffusion rate of soil gases and the gas transport rate, which likewise affects evaporation from the soil surface and temperature distribution on irregular soil surfaces. For some traditional simple closed gas chambers (without pressure balance inside and outside the gas chamber), the monitoring error is significantly high, such as a pressure change of 0.5 Pa results in a 20%-70% deviation in CO 2 flux measurements (Xu et al 2006).
On the one hand, the monitoring chamber may isolate the wind turbulence, reducing the gas exchange rate of the soil boundary layer. To explore this problem, we selected the time period during which the wind turbulence phenomenon was prevalent. We placed the closed air chamber on the pre-installed stainless-steel collar, and determined its isolation turbulence effect according to the pressure difference fluctuation value. Figure 4 shows that during the first 5 min, when the monitoring point was not covered with an air chamber, the differential pressure values on the soil surface fluctuated significantly with wind turbulence. The surface wind speed was high (0-100 s), and the pressure difference also showed an upward trend. At 100-200 s, the wind speed, and the pressure difference also decreased. After 200 s, the wind speed increased instantaneously, and the pressure difference increased immediately. There was a strong correlation between the two variables (R 2 =0.2, P<0.001). At approximately 300 s, a closed gas chamber (without equilibrium differential pressure) was placed on the collar. At this time, the surface wind speed remained at a high level ( figure 4(a)), but the differential pressure value was significantly less than that of during the period of 200-300 s. When the closed gas chamber was removed at 450 s, the differential pressure on the soil surface immediately increased. Thus, in an environment with wind turbulence, the use of a closed chamber with unbalanced differential pressure for On the other hand, when placing and removing the air chamber, the monitoring point produces an abnormal differential pressure, which also affects soil gas emissions. If these influencing factors are not considered when designing the monitoring air chamber, the measured flux results will not represent the actual values. First, when the monitoring chamber was closed and the gasket was compressed, the air pressure within the chamber increased instantaneously (figures 4(b) and 5). At this point, a large amount of gas was pressed into the soil layer to eliminate the increased pressure in the chamber, which affected the original diffusion gradient of CO 2 . As the adjustment of CO 2 under the influence of chamber pressure is primarily a diffusion process, it may take a long time to recover once disturbed Livingston 2001, Xu et al 2006). Second, in the measurement process, the evaporation of water and the increase in temperature in the soil also lead to an imbalance in chamber pressure in the air chamber with unbalanced pressure. According to the ideal gas law (PV=nRT), we estimated that the pressure in the closed gas chamber would change by approximately 333 Pa every time the temperature fluctuates by one degree. In addition, water vapour evaporation can easily cause a change in steam pressure in the closed chamber. These effects cause the monitoring chamber to be under overpressure, which may lead to a serious underestimation of soil carbon flux (Xu et al 2006). Therefore, when using this type of air chamber to monitor soil gas flux and the ambient air pressure changes, the measurement deviation is very large. As the air chamber is isolated from the external environment and the pressure suppression effect of the air chamber is significant, the air pump effect or pressure pump effect caused by wind turbulence is significantly weakened, and the underestimation error increases by several orders of magnitude.

Gas chamber with the designed equilibrium pressure function
When we found that the closed gas chamber without a balanced differential pressure function had a significant isolation effect on wind turbulence, to further understand the effect of a windy environment on the monitoring closed gas chamber with balanced differential pressure function, we simultaneously conducted a control group experiment in the pre-set area. We considered that the other variables were constant, except for the design of the monitoring gas chamber. Figure 6(a) shows the total wind speed at 1 m on the surface during the experiment, and figure 6(b) shows the soil pore pressure difference data of monitoring points 1, 2, and 3 at the same time point; the soil surface without air chamber cover and the soil surface with closed air chamber cover, in which the closed air chamber is divided into balanced and unbalanced pressure differences. According to the data in figure 6(b), in the wind turbulence environment at the same time point, the fluctuation amplitude of the soil pore pressure difference without an air chamber cover was significantly higher than that of with an air chamber cover, which is consistent with the aforementioned analysis results from different times before and after the same place(figure 4). The closed air chamber isolated a part of the wind turbulence. Based on the pressure difference monitoring data for the two closed gas chambers with unbalanced pressure and balanced pressure, the fluctuation amplitude of the pressure difference of the gas chamber with an unbalanced pressure design is less than that of the gas chamber with a balanced pressure design. Thus, the isolation effect of the former on wind turbulence is higher than that of the latter. However, based on the soil pore pressure difference measured for the balanced pressure chamber and without gas chamber, the fluctuation amplitude of the former is significantly lesser than that of the latter. Thus, even the designed monitoring chamber with balanced pressure has a significant isolation effect in high-frequency wind turbulence conditions. Therefore, monitoring instruments that use only a simple ventilation tube to negate the effect of the differential pressure within and outside the air chamber are effective in environments with no disturbance or large timescale pressure changes, that is, where the frequency of perturbed pressure changes in the environment is low. However, under the influence of a strong wind turbulence, the fluctuation frequency of the surface pressure is high, which may lead to the rapid alternation of positive or negative pressure disturbances. Under this condition, the simple balance device had lost its functionality (figure 6). Studies have described this phenomenon both theoretically (Young et al 2001) and experimentally (Kutsch et al 2001).

Relationship between wind turbulence and CO 2 concentration in the air chamber
To explore whether the closed gas chamber had an isolation effect on wind turbulence, we also studied the relationship between wind turbulence and CO 2 concentration in the different gas chambers, that is, the relationship between wind turbulence and soil emissions. As shown in figure 7, during the first 30 s, because the closed gas chamber was placed on the collar for gas monitoring, the CO 2 concentration changed within the chamber slowly, and the total wind speed was relatively low. At 40 s, the wind speed increased significantly, and the CO 2 in the air chamber designed with equilibrium pressure changed immediately, showing an upward trend (the slope of the CO 2 concentration increased); however, the concentration in the air chamber with unbalanced pressure increased slightly. The reason for this phenomenon may be that the downward pressure generated by the air chamber (unbalanced pressure) placed on the collar inhibited the diffusion of soil CO 2 . When the total wind speed increased again at 100 s, the CO 2 concentration in the closed chamber increased by varying degrees. The CO 2 concentration in the chamber with the equilibrium pressure increased significantly, which is consistent with the results reported by Bain et al (2005) and Xu et al (2006). Combined with the analysis of the soil pore pressure difference data for the closed air chamber in figure 6(b), when the wind turbulence causes the surface gas to fluctuate, resulting in the soil pore pressure difference fluctuation (positive and negative), the CO 2 concentration in the air chamber shows an upward trend. This phenomenon explains the aforementioned gas Figure 6. Total wind speed (a) at 1 m from soil; at the same time, the pressure difference between the soil-air interface and 10 cm below the interface for the three conditions of no closed chamber, closed chamber with designed equilibrium pressure function, and closed chamber without designed equilibrium pressure function. Figure 7. Relationship between gas chamber CO 2 concentration and wind. The grey line represents the actual wind speed 1 m from the soil; green and blue curves represent the change in value of CO 2 concentration in the closed air chamber with time in the environment with wind turbulence. The green curve represents the closed air chamber with designed equilibrium pressure function, and the blue curve represents the closed air chamber without designed equilibrium pressure function. dispersion process; that is, with soil pressure fluctuation, gas convection also fluctuates, and the net vertical airflow into and out of the soil is zero. However, |n| is not zero for D e >D s ; this phenomenon shows that the uncertainty caused by wind turbulence on the measurement timescale should be considered when monitoring the gas flux in a closed gas chamber with balanced differential pressure, particularly in the selection and correction of the flux calculation model. This problem was discussed in detail in the calculation model analysis module.

Analysis of the flux calculation model
According to our results for wind turbulence and soil gas emissions, combined with those of the analysis of the gas transport control state diagram in figure 1, the gas dispersion effect caused by wind turbulence is more significant for the common soil (low gas permeability) flux monitoring environment than for the other studied environments. Furthermore, according to the mathematical model, the deviation of the measured value of the reasonably designed closed gas chamber under ambient pressure fluctuations caused by wind turbulence was analysed. First, the effective diffusion coefficient, D e , was determined. According to different soil pore pressure differences, combined with Darcy's law, the gas flow velocity n can be calculated, and the formula is as follows: where k [m 2 ] is the gas permeability, and μ (1.8´10 −5 kg m −1 s −1 ) is the aerodynamic viscosity coefficient. The effective diffusion coefficient, D e , can be obtained using equation (3) (D s is calculated by the Buckingham Palace model, D 0 is 1.64´10 −5 m 2 s −1 ).
The CO 2 concentration data monitored in the field (figure 8) demonstrated that the CO 2 concentration in the air chamber increased nonlinearly with time. At this time, CO 2 concentration inversion was carried out in combination with relevant soil parameters and flux values. It could be observed that the results of linear model deviated greatly from the actual values, while the inversion results of exponential model and polynomial model are better, with root mean square errors of 9.5 mg and 6.9 mg respectively. The results of the concentration segmentation simulation based on equation (7) were similar to the observed data, with a root mean square error of 4.6 mg. In environments with continuous wind turbulence, the nonlinear increase in CO 2 concentration over time within the monitored air chamber is significant, and if a linear model is used for soil carbon flux estimation for this condition, the error will increase further. To explore the error caused by using a linear model to calculate the flux under the influence of continuous wind turbulence, we expanded and analysed a flux calculation model (equation (7)) according to the power series. The expansion formula is as follows: At this time, the linear model was compared with equation (10). We observed that the equation of the linear model was simplified and that all high-order terms of the power series expansion were omitted, leading to the deviation of the calculated flux value f 0 , which is less than the actual flux value, leading to flux underestimation. As shown in figure 9(a), in an environment without wind or pressure fluctuations, the error of the linear model was greater than 4% when the closed air chamber was continuously monitored for 1 min. If the wind causes surrounding pressure fluctuations, the linear model calculation error will be positively correlated with the pressure difference formed by the pressure fluctuation for 1 min, and a pressure difference of 1 Pa will increase the relative error by 1%. Simultaneously, the calculation error of the linear model increased with the measurement time of the air chamber. In a windless environment, the relative error exceeded by 12% when the measurement time was increased to 10 min, and for the same monitoring time, the relative error exceeded 16% Figure 9. (a). For different soil pore pressure differences (different wind turbulence intensity), the relative error between the linear model and the flux calculation model (equation (7)) is a function of time. Data points represent the calculation results of soil total porosity (j) of 0.5, effective porosity (θ) of 0.35, soil gas permeability (k) of 10 −11 m 2 , and dispersion coefficient (a) of 0.1 m. According to the dispersion model, the absolute value of differential pressure (ΔP) was used for error analysis. (b). For different soil pore pressure differences (different wind turbulence intensity), the relative error between the exponential model and the flux calculation model (equation (7)) is a function of time. Data points represent the calculation results of soil total porosity (j) of 0.5, effective porosity (θ) of 0.35, soil gas permeability (k) of 10 −11 m 2 , and dispersion coefficient (a) of 0.1 m. According to the dispersion model, the absolute value of the differential pressure (ΔP) is used for error analysis.
in an environment of continuous wind (1 Pa differential pressure). In a gusty environment, the fitting effect of the linear model is very poor.
For some closed gas chambers fitted with the exponential model, the calculated value deviated significantly from the actual flux value in the wind turbulence environment. The exponential fitting model is expressed as follows: where K is the diffusion rate constant, which is an integrated expression of the effective gas diffusion coefficient. This method often avoid the following phenomenon: over time, the accumulation of CO 2 in the gas chamber leads to a rapid decline in the gas concentration gradient, which affects the fitting of the key parameter K of the calculation model. Therefore, the method obtain the change value of the gas concentration in a sufficiently short time for data fitting, usually approximately 10 s. This processing method is a recognised fitting method in the case of no wind or environmental disturbance, but in the case of wind fluctuation, the fitting value for the first few seconds is used to replace the main parameters of the latter for calculation, and the result deviates from actual values. To analyse the error in this section, we used the calculation model of equation (7) and the assumed soil parameters for the analysis. Assuming that there is no pressure fluctuation in the first 30 s of the measurement process, there is a pressure fluctuation (the pressure difference is 0.5, 1, 1.5, and 2 Pa). The error generated according to the calculation method adopted by the aforementioned model is shown in figure 10. If the monitored soil medium is relatively uniform, that is, when the dispersion coefficient (a) is 0.1 m, air pressure fluctuation will occur on the soil surface, which causes the calculated value of gas flux to be significantly lower than that of the actual flux, and its underestimated value is positively correlated with the differential pressure. That is, the higher the pressure difference, the more evident the flux underestimation effect, and the underestimation value gradually increases with the increase in monitoring time. However, the soil in the real environment is generally a non-uniform medium; thus, the dispersion coefficient (α) will be greater than 0.1 m, with a range of 0.1-0.4 m. At this time, the wind turbulence in the monitoring environment caused fluctuations in the surface pressure, further increasing the measurement error of the closed chamber. As shown in figure 11, with an increase in the dispersion coefficient, when the monitoring time is up to 5 min in the environment with a 1.5 Pa pressure fluctuation, the error value (underestimation) of the aforementioned fitting method for calculating flux will increase from the original 3.1% to 9.2%. For soil with a dispersion coefficient of 0.4 m, the error (underestimated value) will exceed 10% in the environment with a differential pressure fluctuation of 2 Pa for 5 min. Figure 10. In the case when there is no pressure fluctuation for the first 30 s of the measurement process and then pressure fluctuation is introduced (the pressure difference is 0.5, 1, 1.5, and 2 Pa); the error generated by the exponential fitting method is used as a function of time change. Data points represent calculation results of soil total porosity (j) of 0.5, effective porosity (θ) of 0.35, soil gas permeability (k) of 10 −11 m 2 , and dispersion coefficient (a) of 0.1 m. According to the dispersion model, the absolute value of differential pressure (ΔP) is used for error analysis.

Discussion
It is clear that wind turbulence can have an effect on the monitoring of soil fluxes in a confined air chamber. For a simple closed gas chamber without a balanced differential pressure treatment, the monitoring results do not represent the actual flux because any pressure change in the monitoring gas chamber leads to a strong response to the gas. In addition, the simple closed gas chamber exerts a strong isolation effect on wind turbulence, and the result obtained deviates from the actual flux. For a closed gas chamber with a simple design of balanced pressure difference, it also isolates the wind turbulence effect and alters the experimental results in some cases, such as the venturi effect caused by an unreasonable pressure balance opening. Bain et al (2005) and Xu et al (2006) have also mentioned this phenomenon. To test the pressure balance effect of the air chamber, studies have been conducted using the closed air chamber both indoors and outdoors. This method is more effective for studying an air chamber design, but it cannot further evaluate the relationship between wind turbulence and gas emissions. Mohr et al (2020) have connected one end of the differential pressure gauge to the calibration system and the other end to the soil to determine the enhancement effect of wind turbulence, which may effectively avoid the problem of wind blowing directly into the differential pressure pipe. However, there may be a delay in the wind turbulence effect, which amplifies the differential pressure effect. Therefore, to improve the method used to study whether the air pressure fluctuation caused by wind turbulence enhances soil gas emissions, causing monitoring errors in the closed gas chamber, the method of directly detecting the pressure difference between the upper and lower layers of soil was adopted in this study. We found that fluctuations in air pressure led to an increase in the CO 2 concentration in the air chamber. This phenomenon can be interpreted as follows: when the soil pressure is greater than the atmospheric pressure, the gas flows out of the soil, and when the soil pressure is less than the atmospheric pressure, the gas enters the soil. In these two processes, the total volume of gas flowing in and out may remain constant. However, there are often considerable differences in specific gases. The CO 2 concentration in the soil generally ranges from thousands of ppm to tens of thousands of ppm, which is several orders of magnitude higher than that in the atmosphere (400 ppm). This high CO 2 concentration in the soil leads to a significant difference in the mass of CO 2 gas entering and leaving the soil; that is, more CO 2 flows out of the soil than that enters the soil, resulting in an increase in the CO 2 concentration in the gas chamber.
Furthermore, the estimated annual CO 2 emission from the soil into the atmosphere is 98±12 Pg C (Bond-Lamberty and Thomson 2010), which is approximately 15 times the current annual emission from fossil fuel combustion (Denman et al 2007, Goffin et al 2015; that is, an underestimation error of 10% renders the soil CO 2 emission equivalent to global fossil fuel emissions for 1 year. Therefore, for measurement in windy environments, either the air chamber must be improved or the calculation model must be modified. For computational models, model selection is based on experimental data and is not limited to linear and exponential models, whose polynomial models also show excellent computational results. In addition, in environments with high wind turbulence, calculating the flux data in segments may be considered to avoid a Figure 11. On the time scale of 5 min of monitoring, changes caused by wind turbulence cause relative errors in the flux, f 0 , as a function of the variation in soil pore pressure difference. Data points represent calculation results of the soil dispersion coefficient (0.1-0.4 m), total porosity (j) of 0.5, effective porosity (θ) of 0.35, and soil gas permeability (k) of 10 −11 m 2 . According to the dispersion model, the absolute value of differential pressure (ΔP) is used for error analysis. uniform fit affecting the calculation result. If the soil respiration intensity is measured at a particular site, longterm monitoring should be used to eliminate errors by averaging multiple measurements. Regarding the monitoring gas chamber, open-type devices can be designed to ensure that the air pressure inside the chamber is consistent with that of the outside environment and to combine the air pressure fluctuations caused by wind turbulence and gas concentration data for flux calculations. In large turbulent environments, the introduction of the eddy covariance technique can be considered to complete the flux calculation within an area of few square metres.

Conclusion
In an environment with natural wind, wind-induced turbulence causes soil pore pressure to fluctuate, which enhances CO 2 emissions in the soil. This phenomenon explains the gas diffusion dispersion transport mechanism in low-permeability porous media, as described in various studies. If a simple closed air chamber is used to monitor the soil carbon flux in the wind-induced turbulence environment, there will be a significant error in the results because the simple closed air chamber exerts a significant isolation effect on wind turbulence. When selecting the flux calculation model for a closed gas chamber with a fully balanced differential pressure design, a model with a high fitting degree should be used, which reduces the error. In a wind-induced turbulence environment, the turbulence effect renders the linear flux calculation model unsuitable and adds to the increase in error. For the exponential fitting method, in a windy environment, the monitoring error of 5 min can be as high as 6%-10%; that is, there is an underestimation effect compared to the actual flux. If these problems are not solved, they will cause a hindrance in the determination of the ecosystem carbon budget, global carbon budget, and greenhouse effect caused by greenhouse gases. Therefore, for a windy environment, either the air chamber or the calculation model must be improved. Using only one flux calculation model is insufficient, and model selection should be based on experimental data. In environments with high wind turbulence, the flux data can be calculated in segments.