OCCURRENCE OF A NEARLY CONSTANT AIR FLUX THROUGH THE ACCUMULATION CHAMBER AND DETERMINATION OF THE TWO COMPONENTS OF THE CO 2 FLUX FROM SOIL . I : LABORATORY EXPERIMENTS „

Different types of laboratory experiments were carried out during this study. In type A experiments a standard gas mixture is continuously injected, at constant flux, into the accumulation chamber, mimicking the soil CO2 flux measurements performed in field surveys. In type B experiments, a standard gas mixture is initially injected into the accumulation chamber for a short lapse of time, to achieve a relatively high CO2 concentration inside the accumulation chamber; then the injection of the standard gas mixture is stopped and the CO2 concentration inside the chamber is monitored for a sufficient interval of time. In both types of experiments, the accumulation chamber appears to be flushed by a considerable flux of atmospheric air, which is virtually constant in each experiment but is different from experiment to experiment. The occurrence of this air flux through the accumulation chamber (i) has no effect on the determination of the soil CO2 flux on the basis of the initial slope (at time zero) of the CO2 concentration-time curve, but (ii) it complicates the evaluation of the two components of the soil CO2 flux, namely the CO2 molar fraction of soil gas and the flux of the soil gas mixture. A method to obtain both the CO2 molar fraction of soil gas and the flux of the soil gas mixture is presented and the implications related to the knowledge of the two components of the soil CO2 flux are discussed. et al, 2007; Padrón et al., 2008b; Viveiros et al., 2008, 2009, 2010; Perez et al., 2012; Rinaldi et al., 2012; Lewicki and Hilley, 2014; Padilla et al., 2014; Werner et al., 2014]. Consequently, surveys of FCO2 have to be carried out under dry and stable weather conditions to avoid the detrimental effects caused by variations of meteorological parameters. Use of the accumulation chamber may change the soil gas flow from its natural undisturbed state by altering the gas pressure inside the chamber, varying the pressure and concentration gradients in the underlying soil, diverting the soil gas flow around the chamber, altering locally soil physical properties (e.g., by inserting a “collar” into the soil to position the chamber), and determining an increase of water vapor within the chamber [Norman et al., 1992; Healy et al., 1996; Evans et al. 2001; Gerlach et al. 2001; Welles et al. 2001]. These effects has been quantified through controlled laboratory tests, showing that measured FCO2 values are 0-25% lower than the imposed FCO2 values, in the range 200 12,000 g m-2 day-1 [Evans et al., 2001]. However, these uncertainties can be mitigated by imposing known FCO2 values and calibrating the system accordingly [Chiodini et al., 1998]. All in all, taking suitable precautions and accepting some minor uncertainties, the accumulation chamber method had been shown to be effective in determining the soil FCO2 values from the low values sustained by decay of organic substances to the high values in areas of steaming ground [Chiodini et al., 1998; Norman et al., 1992, 1997; Lewicki et al., 2005; Lewicki and Hilley, 2014]. In spite of the impressive number of studies carried out in the last 25 years, the potential uses for flux data determined using the accumulation chamber method have not been fully exploited. For instance, the accumulation chamber CO2 time series can be used, in principle, to obtain not only the FCO2 value but also its two components, namely the molar fraction of CO2 in the soil gas, XCO2,G, and the flux of the soil gas mixture, FG. Note that only two of the three variables FCO2, FG, and XCO2,G are independent, as they are linked by the simple relation:

Use of the accumulation chamber may change the soil gas flow from its natural undisturbed state by altering the gas pressure inside the chamber, varying the pressure and concentration gradients in the underlying soil, diverting the soil gas flow around the chamber, altering locally soil physical properties (e.g., by inserting a "collar" into the soil to position the chamber), and determining an increase of water vapor within the chamber [Norman et al., 1992;Healy et al., 1996;Evans et al. 2001;Gerlach et al. 2001;Welles et al. 2001].These effects has been quantified through controlled laboratory tests, showing that measured F CO 2 values are 0-25% lower than the imposed F CO 2 values, in the range 200 -12,000 g m -2 day -1 [Evans et al., 2001].However, these uncertainties can be mitigated by imposing known F CO 2 values and calibrating the system accordingly [Chiodini et al., 1998].
All in all, taking suitable precautions and accepting some minor uncertainties, the accumulation chamber method had been shown to be effective in determining the soil F CO 2 values from the low values sustained by decay of organic substances to the high values in areas of steaming ground [Chiodini et al., 1998;Norman et al., 1992Norman et al., , 1997;;Lewicki et al., 2005;Lewicki and Hilley, 2014].
In spite of the impressive number of studies carried out in the last 25 years, the potential uses for flux data determined using the accumulation chamber method have not been fully exploited.For instance, the accumulation chamber CO 2 time series can be used, in principle, to obtain not only the F CO 2 value but also its two components, namely the molar fraction of CO 2 in the soil gas, X CO 2 ,G , and the flux of the soil gas mixture, FG.Note that only two of the three variables F CO 2 , F G , and X CO 2 ,G are independent, as they are linked by the simple relation: (1) In addition, the occurrence of gas exchange between the atmosphere and the accumulation chamber needs to be investigated.This paper discusses (1) the results of suitable laboratory experiments aimed at investigating gas exchange between the atmosphere and the accumulation chamber, (2) a method to obtain F G and X CO 2 ,G from the CO 2 time series acquired by means of the accumulation chamber method, and (3) the implications related to the knowledge of the two components of F CO 2 , in order to underscore why it is important to know not only F CO 2 but also F G and X CO 2 ,G .

THE LABORATORY EXPERIMENTS
In this work, all the laboratory experiments were performed using West Systems portable CO 2 fluxmeters comprising the following main components (Figure 1): (a) A West Systems™ accumulation chamber of type A, equipped with both a 80 rpm fan, to ensure the homogenization of the gas mixture inside the chamber, and a pressure compensation device to maintain pressure equilibrium between inside the chamber and the surrounding air outside the chamber, avoiding the pressurization of the chamber that would alter the gas flow from soil (see above).(b) A non-dispersive infrared spectrometer as CO 2 analyzer, either a LICOR LI-820™ or a Vaisala CAR-BOCAP® CO 2 sensor GMP343.The CO 2 analyzer performs the continuous determination of CO 2 concentration inside the accumulation chamber.
The main technical specifications of the LICOR LI-820™ are: measurement range 0-20,000 ppmv; root mean square noise <1 ppmv at 370 ppmv with 1 s signal filtering; accuracy 3% of reading.
The main technical specifications of the Vaisala GMP343™ are: measurement range 0-20,000 ppmv; noise at 370 ppm CO 2 ± 3 ppmv CO 2 ; accuracy ± (5 ppmv + 2% of reading).(c) A membrane pump that provides continuous transfer of the gas from the accumulation chamber to the CO 2 analyzer and back into the chamber through the inlet and outlet tubes.The fluxmeters were equipped with one of the following three pumps KNF NMP830, KNF NF30, and KNF NMS020.The flowrate of each pump was measured with an accuracy close to 1% by using a Gilian Gilibrator-2 NIOSH Primary Standard Air Flow Calibrator, obtaining the following values: 47.5 cm3 s -1 for KNF NMP830, 35.5 cm 3 s -1 for KNF NF30, and 24.2 cm 3 s -1 for KNF NMS020.(d) A palmtop computer for data acquisition with the frequency of one record per second.Acquired data include: time, CO 2 concentration, pressure and temperature in the measuring cell of the CO 2 analyzer, ambient temperature and barometric pressure.Cell pressure and barometric pressure are recorded only by the fluxmeter equipped with the LICOR LI-820™ CO 2 analyzer.Further details are given by the handbook of the West Systems CO 2 fluxmeter (https://www.westsystems.com/wp-content/uploads/2018/01/Handbook_Portable_8.2.pdf).The fluxmeter comprising the accumulation chamber, the inlet and outlet tubes, the cell of the CO 2 analyzer and filters has a net total volume of 3063 cm3, whereas the accumulation chamber has a basal area of 314 cm 2 .
In the adopted experimental set up (Figure 2a), the accumulation chamber is positioned with the opening on a desk, either inserting a rubber gasket over its rim (Figure 2b), to minimize the possible input of atmospheric air (see below), or without a gasket.The desk surface is impermeable to air and is equipped with a gas injection point which conveys the standard gas mixture, at the selected flux, from the cylinder to the accumulation chamber.
Three types of experiments were performed, called A, B, and C. In type A experiments, the standard gas mixture is continuously injected into the accumulation chamber keeping the gas flux constant at the selected value.These experiments mimic the F CO 2 measurements performed in field surveys.
In type B experiments: (1) the standard gas mixture is injected into the accumulation chamber for a short in-terval of time, typically 100-120 s, to achieve a CO 2 concentration inside the accumulation chamber of ∼7000 ppmv; (2) the gas injection is stopped, and the fluxmeter continues to operate to monitor the CO 2 concentration inside the chamber for an interval of time, typically 1900-2100 s.These experiments are used to understand if the accumulation chamber is flushed or not by atmospheric air and to quantify the air flux if any.
The type C experiments are similar to those of type B. The only difference is the use of plaster to seal both the chamber -desk interface and the pressure compensation device (Figure 2c).These experiments are utilized to verify the absence of gas leaks.
The three different standards were used in the three different types of experiments but no difference in behavior was observed when different standards were used.

METHODS OF INTERPRETATION OF CO 2 TIME SERIES
To interpret the CO 2 time series acquired during the laboratory experiments the system is modeled as a perfectly-mixed single box.Two distinct mass balances can be written as detailed below.In this communication, simple mass balances involving the total soil-chamber-atmosphere CO 2 mass exchanges are preferred to equations in which the diffusive and advective components of the soil gas flux are considered separately [e.g., Welles et al., 2001] due to the ambiguities in the characterization and separation of these two distinct components.
Approach (1) is based on the hypothesis that the accumulation chamber is not flushed by atmospheric air.It means that the flux of the standard gas mixture entering the accumulation chamber is balanced, at any time, by the flux of gas mixture leaving it through either the space between the chamber rim and the desk or the pressure compensation device or both.This hypothesis was adopted by Chiodini et al. [1998].
Approach ( 2) is based on the assumption that the gas mixture leaving the accumulation chamber comprises the standard gas mixture plus a flux of atmospheric air.In other terms, the accumulation chamber is considered to be flushed by a continuous flux of the standard gas mixture and a continuous flux of atmospheric air.The need to invoke approach (2) will become apparent in the following discussion.

METHODS OF INTERPRETATION OF CO 2 TIME SERIES: APPROACH (1)
The CO 2 time series for approach (1) is described by the following Equation [e.g., Leib et al., 2008]: (2) where: t (s) stands for time, V (cm 3 ) is the volume of the flux meter comprising the accumulation chamber, the inlet and outlet tubes, the cell of the CO 2 analyzer and filters, X CO 2 ,t+dt and X CO 2 ,t (mol/mol) designate the CO 2 molar fraction in the accumulation chamber at time t+dt and at time t, respectively, X CO 2 ,G (mol/mol) represents the CO 2 molar fraction of the standard gas mixture, F G and F out (cm 3 s -1 ) stand for the flow rates of the standard gas mixture entering and leaving the accumulation chamber, respectively, which are assumed to be equal to each other, that is: (3) Dividing both sides of Equation ( 2) by V and considering that X CO 2 ,t+dt -X CO 2 ,t = dX CO 2 , Equation ( 2) can be rearranged as follows:

METHODS OF INTERPRETATION OF CO 2 TIME SERIES: APPROACH (2)
To take air inputs into consideration, Equation (2) has to be modified as follows: (5) where X CO 2,A (mol/mol) represents the CO 2 molar fraction of atmospheric air, F A (cm 3 s -1 ) is the flow rate of atmospheric air entering the accumulation chamber.
Equation ( 5) assumes that, at any time, the sum of the standard gas mixture flux and atmospheric air flux is equal to gas flux leaving the accumulation chamber.Again, dividing both sides of Equation ( 5) by V and considering that , it can be rewritten as follows: (6) 6) is a first order linear ordinary differential Equation, whose general solution is: where k is a constant.To find k, t is set equal to zero, obtaining: (8) where X CO 2 ,O is the initial value of the CO 2 molar fraction inside the accumulation chamber.Hence, Equation ( 7) can be rewritten as follows: (9) Equation ( 9) represents the theoretical basis for the method used in section 4.1 to obtain F G and X CO 2 ,G from the accumulation chamber CO 2 time series.

THE TYPE C EXPERIMENTS
For all the type C experiments, the CO 2 concentration-time curve includes: (1) a quick build up determined by the rate of CO 2 input into the accumulation chamber, followed by (2) flattening of the curve due to the almost constant CO 2 content after ending the CO 2 input into the accumulation chamber (Figure 3).Since plaster is not totally impermeable to gases, the CO 2 concentration-time curve deviates from the ideal of constant CO 2 content.The decrease in CO 2 concentration with time, although very small, depends on the flowrate of the membrane pumps, F P , with values of (a) -1.1 • 10 -7 to -2.6 • 10 -7 s -1 for runs 2 and 4, for a membrane pump flowrate of 24.2 cm 3 s -1 , and (b) -3.4 • 10 -7 to -5.0 • 10 -7 s -1 for runs 1 and 3, for a pump flowrate of 47.5 cm 3 s -1 .The average difference between the atmospheric pressure and the pressure in the cell of the LICOR LI-820™ CO 2 analyzer, ΔP*, was 43.4 mbar in run 1, 19.2 mbar in run 2, 43.9 mbar in run 3 and 18.9 mbar in run 4.

THE TYPE B EXPERIMENTS
The CO 2 concentration-time curve for all type B experiments comprises a fast build up caused by the injection of CO 2 , followed by a relatively slow drawdown, upon cessation of the CO 2 injection into the accumulation chamber (Figure 4).The CO 2 injection was performed at flowrates similar to those adopted in type C experiments.The buildup curve does not give any information of interest.In contrast, the form of the drawdown curve, with decrease of CO 2 concentration with time and negative slope also decreasing with time, indicates that the accumulation chamber is continuously flushed by atmospheric air.In fact, in the absence of such atmospheric air flush, the CO 2 concentration inside the accumulation chamber would be expected to remain constant or nearly so at the maximum value achieved due to CO 2 injection into the chamber, as it is observed in the experiments of type C (see section 3.1).
In addition to this important qualitative information on the gas exchanges between the atmosphere and the accumulation chamber, the drawdown curve was used to determine by trial and error the flux of atmospheric air flushing the chamber assuming that it is constant.The sought solution corresponds to the minimum of the average absolute deviation (AAD) between measured X CO 2 ,t values and calculated X CO 2 ,t values from Equation (5).
Both the measured CO 2 concentrations and the corresponding calculated CO 2 values are plotted against time for the two experimental runs of type B 152131 and 161126 in Figure 4. Run 152131 (Figure 4a) utilized a Plot of the measured CO 2 concentration inside the accumulation chamber versus time for four experiments of type C, in which plaster was used to seal both the chamber -desk interface and the pressure compensation device.
rubber gasket placed over the rim of the accumulation chamber, whereas there was no gasket for run 161126 (Figure 4b) where the accumulation chamber was placed over the gas injection point and sat directly on the desk.For both runs there is a perfect match between the measured drawdown curve and the calculated counterpart, with an AAD of 0.26% and a maximum absolute deviation (MAD) of 1.2% in the run with the rubber gasket and with an AAD of 0.38% and a MAD of 1.5%, in the run without the gasket.The main results of the experimental runs of type B, including those depicted in Figure 4, are reported in Table 1, showing that there is a very good correspondence between the measured drawdown curves and the calculated counterparts, with AAD values of 0.14 to 1.54%.Since the X CO 2 ,t values computed using Equation ( 5) reproduce with acceptable accuracy the corresponding measured X CO 2 ,t values, the starting hypothesis is satisfied, i.e., the flux of atmospheric air flushing the accumulation chamber during the experiments of type B can be considered to be virtually constant.
Table 1 also shows that F A represents 1.4 to 2.8 % of F P in the experiments with the rubber gasket, whereas F A constitutes 2.2 to 4.7 % of F P in most experimental runs without the gasket, apart from run 144401, with F A equal to 1.4% of F P , and run 122850, with F A equal to 6.6% of F P .The lower F A /F P ratios of the experiments with the rubber gasket are not surprising since the gas-ket acts as a partial seal and reduces the flow of air entering the accumulation chamber.

THE XCO 2 TIME CURVE OF TYPE A EXPERI MENTS
Plots of CO 2 concentration versus time are shown in Figure 5 for four selected type A experiments, 103212, 154723, 112311, and 141306, all with F G in the range 1.67 to 6.67 cm 3 s -1 .
In these plots, the measured CO 2 time series (black line) are compared with the corresponding CO 2 time series calculated using: (i) Equation (2), i.e., assuming that the accumulation chamber is not flushed by atmospheric air (blue curve) and (ii) Equation ( 5), i.e., assuming that the accumulation chamber is flushed by a constant flux of atmospheric air (red curve).Again, since the flux of atmospheric air through the chamber is unknown, it was obtained by trial and error until the AAD between measured and computed data attains the minimum value.
These CO 2 -time plots show that results calculated using Equation (2) overestimate significantly the measured CO 2 time series, whereas results computed using Equation (5) closely approximate the measured CO 2 time series.Note that the agreement between the measured and calculated results for a constant flux of atmospheric air are very good for the three type A experiments 103212, 154723, and 112311, of duration ranging between ∼600

DETERMINATION OF THE SOIL CO 2 FLUX COMPONENTS
and ∼1800 s (Figure 5a, b, and c, respectively).In contrast, the agreement for type A experiment 141306, with a much longer duration, ∼7000 s is less satisfactory (Figure 5d).Results show a crossover between the measured data curve and the computed curve (for a constant flux of atmospheric air) that might be due to the moderate decrease of the atmospheric air flux with time, an effect which is evidently detectable only in experiments of long duration at these F G values.
The main characteristics of some experimental runs of type A, with F G in the range 1.67 to 6.67 cm 3 s -1 , including those displayed in Figure 5, are reported in  4. ΔP* is the average difference between the atmospheric pressure and the pressure in the cell of the LICOR LI-820™ CO 2 analyzer.These data are not available for the Vaisala CARBOCAP® CO 2 analyzer.(iii)consequently, the F A /(F A +F G ) ratio decreases gradually from 0.52-0.60 at F G of 1.67 cm 3 s -1 to 0.08 at F G of 6.67 cm 3 s -1 .Type A experiments with F G in the range 0.0833 to 0.833 cm 3 s -1 :

Code
(i) have higher AAD between measured and computed data, (ii) exhibit a crossover between the measured data line and the computed curve, (iii)have high F A values, in the range 5 to 10 cm 3 s -1 , and (iv) have, therefore, high F A /(F A +F G ) ratios, from 0.85 to 0.99.Since the results for the type A experi-ments with F G in the range 0.0833 to 0.833 cm 3 s -1 are affected by relatively high uncertainties, whose origins are not properly understood, they are not considered in the following discussion.

DISCUSSION
The accumulation chamber was flushed by atmospheric air in all the laboratory experiments of type A and B. F A is virtually constant in each type B experiment as well as in each type A experiment of duration lower than 1800-2000 s, but F A is different from experiment to experiment.

HERNÁNDEZ-RODRÍGUEZ ET AL.
FIGURE 5. Plot of CO 2 concentration in the accumulation chamber versus time for four selected experiments of type A showing the measured CO 2 time series (black line), the CO 2 time series calculated using Equation (2), i.e., assuming that the accumulation chamber is not flushed by atmospheric air (blue curve), and the CO 2 time series calculated using Equation ( 5), i.e., assuming that the accumulation chamber is flushed by a constant flux of atmospheric air (red curve).
The occurrence of this considerable air flux through the chamber raises some questions, the first and most important is does the air flux affect the determination of F CO 2 ?To answer this question, it must be noted that Equation ( 6), which incorporates the air flux through the chamber, reduces to; (10) at the initial conditions, i.e., at time zero.Equation ( 10) corresponds to Equation (7) of Chiodini et al. [1998] which is used to evaluate F CO 2 on the basis of the initial slope (at time zero) of the CO 2 concentration-time curve.The only difference between these two Equations is the physical dimension (and consequently the measurement unit) of Chiodini et al. [1998] and [volume • time -1 ] in this work.Leaving aside this difference, the important thing to be noted is that F A does not appear in Equation ( 10) and, therefore, the flux of air through the accumulation chamber has no effect on the determination of the F CO 2 .A second question is what are the entry and exit points through which air enters and leaves the chamber?Before answering this question it must be recalled that maintenance of pressure equilibrium between inside the chamber and the surrounding air outside the chamber is a necessary requirement so that the measured F CO 2 and its two component terms (F G and X CO 2,G ) can be truly representative of the natural values [e.g., Xu et al., 2006].For this reason, the chamber is equipped with a pressure compensation device.For the same reason, an effective seal cannot be emplaced between the chamber and either the soil surface in field deployment or the desk surface in laboratory tests (2) .Only a gasket can be used to minimize the inflow of atmospheric air during the measurements, as done in some experiments of type A and B (see above).Therefore, it can be assumed that atmospheric air may enter and leave the accumulation chamber through both the interface between the chamber rim and the surface onto which the chamber rests and the pressure compensation device.
The second pathway is considered less likely unless the pressure inside the chamber, P AC , attains a value significantly higher than the external atmospheric pressure, P atm .The data obtained during the experiments of type B and C carried out using the LICOR infrared spectrometer can be used to evaluate the difference ΔP = P atm -P AC , since both P atm and the pressure in the measuring cell of the LICOR CO 2 analyzer, Pcell, are continuously recorded during these runs.As noted earlier, pressure data are not available for the experiments performed using the Vaisala CARBOCAP CO 2 analyzer.Hence, the difference ΔP* = P atm -P cell can be computed.ΔP* can be considered a proxy of ΔP assuming that P cell is similar to P AC .Since the oscillations of ΔP* during the experi ments are in the order of ∼1 mbar, ΔP* data were averaged and reported in Table 1 for the experiments of type B and in section 3.1 for the experiments of type C. The results show the average ΔP* results are strongly dependent on F P (Figure 7) as described by the following linear regression Equation (ΔP* in mbar, F P in cm 3 s -1 , N = 12, R 2 = 0.963): The dependence of ΔP* on F P suggests that the pumping rate controls the pressure distribution in the measuring systems during the experiments of types B and C.
A third question is what controls F A ?To answer this question let us consider the plot of F A vs. F P for the type B experiments (Figure 8) for the time after the gas flow is turned off and the only flow is driven by the membrane pump circulating gas from the accumulation chamber to the CO 2 analyzer and back.
Figure 8 shows that the spread of points is limited for the type B experiments with the rubber gasket, whose F A and F P data fit the following linear regression Equation through the origin (R = 0.722): The R value, 0.722, is significant at probability < 5% for N-2 = 6 degrees of freedom, suggesting that the relation between F A and F P is statistically meaningful.In contrast, the type B experiments without the gasket show a remarkable spread of points, also considering that experiment 122850 is not plotted in Figure 8 due to the high F A , 3.13 cm 3 s -1 , and the high AAD, 1.54% (Table 1).The F A and F P values for the type B experiments without the gasket fit the following linear regression Equation through the origin (R = 0.622) The R value, 0.622, is not significant at 10% of probability for N-2 = 5 degrees of freedom, suggesting that the relation between F A and F P is statistically meaningless.
Equation ( 12) has a slope lower than that of Equation ( 13) since as noted above, the rubber gasket acts to some extent as a seal, reducing the flux of air through the chamber.The poor relation between F A and F P for the type B experiments without the gasket is probably due to the variable size of the cross-sectional area available for air flow, reflecting the irregularities of the desk surface onto which the chamber is positioned from one experiment to another.In contrast, use of the rubber gasket seems to decrease the variability of the cross-sectional area to air flow.Irrespective of the somewhat erratic results of the experimental runs without the gasket, there is no doubt that the membrane pump flowrate, F P controls the air flux, F A , in all the type B experiments.
In type A experiments with F G in the range 1.67 to 6.67 cm 3 s -1 and with durations lower than 1800-2000 s, F A appears to be strictly related to F G as shown in Figure 6.It must be noted that in type A experiments there is both a gas flow entering the chamber from below and a gas flow driven by the membrane pump.Consequently, the gas exchanges between the chamber and the atmosphere are probably more complex than in the experiments of type B. In spite of these complexities, for type A experiments F A is neither a random effect nor a noise, but it is due to the unavoidable gas exchange between the chamber and the atmosphere.This gas exchange must be taken into account in order to use the measured CO 2 time series to estimate F G and X CO 2,G .

A METHOD TO OBTAIN F G AND XCO 2,G
To obtain the two components of the soil CO 2 flux, the accumulation chamber CO 2 concentration data are fitted against time adopting Equation (9) as theoretical model, treating F G , X CO 2,G , and F A as adjustable coefficients, and assuming that X CO 2,A is equal to X CO 2,0 (3) .The results of some type A experiments are used to test this method by comparing the known F G , X CO 2,G , and values with the corresponding computed values.cm 3 s -1 , and its high AAD, 1.54% (Table 1).
Table 3 shows those results and two sets of F A values, obtained through use of Equation 9, described in this section and Equation 5, outlined in section 3.3.Also listed in Table 3 is the percent deviation, %dev, which is calculated with respect to the known value for F G , X CO 2,G , and F CO 2 and using the average of the two computed values for F A because the true value is unknown.The average of the absolute values of %dev, is 4.7% for F G , 1.5% X CO 2,G , 5.8% for F CO 2 , and 12.4% for F A .Based on these data, it can be concluded that the adopted method reproduces F G , X CO 2,G , and F CO 2 with acceptable approximations.The larger uncertainties on F A derive from the two distinct approaches adopted to compute the two F A series.In any case, the uncertainties on F A determine related uncertainties on F G and X CO 2,G but do not affect the validity of the method proposed here to obtain the two components of the soil CO 2 flux.The use of this method in the field requires further tests representing the subject of a separate communication.

IMPLICATIONS
There are at least two important implications that come from having knowledge of F G , and X CO 2,G , the two components of F CO 2 .Through the use of bivariate statistics and geostatistics on these data our understanding of the natural systems of interest can be improved to a significant extent.For instance, it should be possible to understand if high , or (c) low values of both parameters.
The other implication is the proper interpretation of isotopic data, which has been the subject of several recent papers [e.g., Chiodini et al., 2008;Parks et al., 2013;Lee et al., 2016;Robertson et al., 2016;Hutchison et al., 2016].To discuss this point, let us assume that two gas samples are collected from the accumulation chamber, as was done by Chiodini et al. [2008].The first sample (sample A) is collected after a few seconds to allow homogenisation of the gas mixture inside the chamber, whereas the second sample (sample B) is collected some time later, at higher CO 2 concentration.Both samples are then analyzed for the δ 13 C CO 2 value.The X CO 2 and δ 13 C CO 2 value of the two samples constrain the mixing line between pure soil gas and air, which is a straight line in the plot of δ 13 C CO 2 vs. the inverse of X CO 2 [Faure, 1986], as schematically shown in Figure 9.
This plot also shows that it is possible to reconstruct the δ 13 C CO 2 value of soil gas, δ 13 C CO 2,G , by reading the δ 13 C CO 2 value corresponding to X CO 2 along the mixing line between pure soil gas and air.This is why knowing the CO 2 concentration of soil gas is of utmost importance for the proper interpretation of the δ 13 C CO 2 values of soil gas -air mixtures collected inside the accumulation chamber.Alternatively, one can wait until the gas inside the accumulation chamber is presumably constituted by pure soil gas or almost so and sample it to obtain a representative δ 13 C CO 2 value.However, this might be a tedious, very long procedure and, moreover, it is difficult to check if the gas inside the accumulation chamber is actually representative of soil gas or not without knowing X CO 2 .Of course this discussion only applies for studies when gas samples for chemical and isotopic analyses of CO 2 are collected from the accumulation chamber, and isn't needed when soil gases are sampled using a probe to penetrate the soil to a suitable depth [e.g., Salazar et al., 2001;Federico et al., 2010;Dionis et al., 2015] values for some experimental runs of type A. The F A values computed by means of the method discussed in this section and that of section 3.3 are also listed..

CONCLUSIONS
Three distinct types of laboratory experiments were performed to investigate gas exchanges between the atmosphere and the accumulation chamber and to implement a method to obtain F G and X CO 2,G , from CO 2 time series data.
The results from the experiments show a considerable air flux through the chamber that is practically constant in each run but differs from run to run.
It seems likely that the interface between the chamber rim and the surface represents the main entry and exit route for atmospheric air.The difference between atmospheric pressure and the pressure in the measuring cell is strongly linearly correlated with the pump flowrate and suggests that the air flux through the chamber is controlled by the membrane pump.In spite of the air flux we find it does not affect the determination of soil CO 2 fluxes, but does complicate assessment of F G and X CO 2,G .A method to compute both the CO 2 molar fraction of soil gas and the flux of the soil gas mixture from CO 2 time series is presented.The data are useful to provide a better understanding of the gas flux in natural systems and are needed for studies when chamber gas is collected for 13 C-CO 2 analyses.

FIGURE 1 .
FIGURE 1.The West Systems portable CO 2 flux meter (from the Handbook of the West Systems CO 2 fluxmeter).

FIGURE 4 .
FIGURE 4. Plot of the measured and computed CO 2 concentration inside the accumulation chamber versus time for two experimental runs of type B 152131 and 161126.Run 152131 (a) was performed inserting a rubber gasket over the rim of the accumulation chamber whereas run 161126 (b) was carried out placing the accumulation chamber directly on the desk over the gas injection point without any gasket.

FIGURE 6 .FFIGURE 7 .
FIGURE 6. Plot of F A vs. F G for some experiments of type A, with F G in the range 1.67 to 6.67 cm3 s-1.The exponential model was adopted to fit the F A and F G- values since the squared regression coefficients is higher than for other models.Closed symbols identify experiments with the gasket whereas open symbols refer to experiments without the gasket.

FIGURE 8 .
FIGURE 8. Plot of the air flux, F A , vs. the membrane pump flowrate, F P for the experiments of type B with the rubber gasket and without it (see legend).Experiment 122850 is not plotted due to its high F A , 3.13

( 3 )
ALTERNATIVELY, ASSUMING A CONCENTRATION OF 400 PPMV FOR AIR (THE PRESENT ATMOSPHERIC VALUE) LEADS TO NEGLIGIBLE CHANGES IN CALCULATION RESULTS.

FIGURE 9 .
FIGURE 9. Plot of the d 13 C value of CO 2 vs. the inverse of the CO 2 molar fraction for two soil gas -air mixtures collected inside the accumulation chamber, samples A and B, which constrain the soil gas -air mixing line (red dashed line).The inverse of the CO 2 molar fraction of soil gas (Soil gas 1) allows one to estimate the 13 C value of CO 2 of soil gas, following the blue dashed line with arrow.Other soil gas compositions (Soil gas 2, 3, 4, and 5) are used to discuss the error on the computed d 13 C value of CO 2 based on the assumption that soil gas is constituted by pure CO 2 (see text).

TABLE 1 .
Main characteristics of some experimental runs of type B. The experiments with code in bold are displayed in Figure

TABLE 2 .
Main characteristics of some experimental runs of type A with F G of 1.67-6.67cm 3 -1 .The experiments with code in bold are displayed in Figure5.

OF THE SOIL CO 2 FLUX COMPONENTS
. 11DETERMINATION

TABLE 3 .
Known and computed F G , X CO 2 ,G , and F CO 2