Improved Membrane Inlet Mass Spectrometer Method for Measuring Dissolved Methane Concentration and Methane Production Rate in a Large Shallow Lake

: Natural water bodies, such as lakes, rivers, and oceans, are important sources of atmospheric methane (CH 4 ). Therefore, quantitative and accurate determination of the dissolved CH 4 concentration in water is of great signiﬁcance for studying CH 4 emissions and providing an in-depth understanding of the carbon cycle. Headspace gas chromatography (HGC) is the traditional method for measuring CH 4 in water. Despite its long success, it has a lot of problems in use, such as complex pretreatment and a long measurement time, and it is not suitable for the CH 4 determination of a large number of samples. In view of these shortcomings, a more convenient and efﬁcient method based on membrane inlet mass spectrometry (MIMS) for quantitative measurements of the dissolved CH 4 concentration in water was established. In our study, the standard curves showed that the method had high accuracy, both at low and high CH 4 concentrations. After a laboratory test, to evaluate the sensitivity of this method, samples were collected from a large shallow lake (Lake Taihu). Both the HGC method and MIMS method were used to determine the dissolved CH 4 to compare these two methods. The small difference in CH 4 concentration obtained from the MIMS and HGC methods and the signiﬁcant correlation between the CH 4 concentrations derived from the MIMS method with those derived from the HGC method showed that the MIMS method could replace the HGC method in the determination of dissolved CH 4 in natural waters. In addition, we also measured the sediment CH 4 production rates in three different areas of Lake Taihu using a laboratory incubation experiment. During the experiment, signiﬁcant CH 4 accumulations were observed, indicating that sediment CH 4 production was an important source of dissolved CH 4 in the water column. Our study concluded that the MIMS method was sufﬁcient and a better alternative than the HGC method owing to its capacity to measure a broad range of values plus the fact that it was relatively easy to use with less manipulation of the samples.


Introduction
Greenhouse gases mainly include methane (CH 4 ), carbon dioxide, and nitrous oxide, which can lead to the greenhouse effect, which is having a significant impact on the natural ecosystem, such as climate anomalies, melting glaciers, and increasing sea levels [1][2][3][4]. Although the CH 4 concentration in the atmosphere is very low compared with carbon dioxide, the greenhouse effect of CH 4 is more than 21-23 times that of carbon dioxide [5].
As important sources of CH 4 , natural water bodies, such as lakes, oceans, and reservoirs, have attracted much attention [6,7]. Therefore, there is a great demand for determining the dissolved CH 4 concentrations in waters. Although the concentration of CH 4 in waters cannot be used to directly quantify the CH 4 emissions to the atmosphere, it can reveal the potential of CH 4 diffusion from waters to the atmosphere. In addition, the CH 4 diffusive flux can be calculated through Fick's first law if we know the dissolved CH 4 concentration, corresponding water temperature, salinity, and wind speed [7,8], which indicates that if we can quickly and accurately determine the concentration of the dissolved CH 4 , it seems to be simpler and more convenient to calculate the CH 4 diffusion from natural waters. Meanwhile, an accurate and effective method for the determination of dissolved CH 4 can help us to estimate the CH 4 production or oxidation capacity in waters, which is of great significance to the study of the fate of CH 4 .
Traditionally, the main method for the determination of CH 4 in water is headspace gas chromatography (HGC), which requires complex pretreatment [9]. The HGC method is widely used in the determination of CH 4 and nitrous oxide in natural water bodies [10,11], but this method cannot directly measure the concentration of dissolved CH 4 in waters, resulting in low efficiency. Thus, a more convenient and efficient method is desired. Although CH 4 measurements using MIMS go back to the 1980s [12], this technique has not been generally used for environmental water sample measurements. As a relatively new method in environmental science for measuring dissolved gases in water, membrane inlet mass spectrometry (MIMS) has attracted much attention owing to its high precision, convenience, and efficiency. MIMS instruments can be configured with a variety of membrane interfaces, including probes, flat membranes in chambers, and flow-through tube membranes [13]. Using a tube membrane with a highly stable flow and temperature control results in highly stable signals with very high precision of gas ratios (better than 1 per mil). This form of MIMS has become the standard for measuring the N 2 /Ar ratio and 15 N in denitrification studies, which require very high precision measurements [14]. MIMS has had limited use for measuring CH 4 in environmental samples and the vast majority of aquatic CH 4 studies utilize alternative methods, such as gas chromatography (GC). Given the high precision and convenience of MIMS for measuring dissolved air gases using the standard methods for denitrification [15,16], we evaluated this analytical approach for CH 4 detection in lake water samples. A recent study used the MIMS method to measure the CH 4 concentration in culture experiments by using the ratio relative to Ar (CH 4 :Ar ratio) [17]. However, this calculation method has a great problem in that the Ar determination using the MIMS method can be greatly affected by the O 2 concentration [18]. Here, we used the standard curve method to accurately calculate the dissolved CH 4 concentration based on the MIMS method.
With the considerations mentioned above, we tested the reliability of the MIMS method for measuring the CH 4 concentration in the laboratory. Furthermore, we also sampled water samples from a large shallow lake, namely, Lake Taihu, to verify that this method is also suitable for dissolved CH 4 concentration measurement in natural waters. Sediment cores were also collected from Lake Taihu to quantify the sediment CH 4 production rate to show that this method is appliable in culture experiments.

CH 4 Measurement Approach Using MIMS
MIMS uses a sampling probe or water sampler equipped with a gas-permeable membrane that separates the water sample from the vacuum of the mass spectrometer. The MIMS in this study (Bay Instruments) includes a tube membrane inside the vacuum inlet ( Figure 1). Water samples are pumped through stainless steel tubing in a thermostated bath (20 • C) prior to entering the vacuum inlet where the membrane tube resides. The flux of dissolved gases across the membrane depends on the flow velocity and temperature and these parameters were held constant. All samples were measured at 20 • C. The gas stream was dried using a liquid nitrogen U-tube trap prior to entering the mass spectrometer. The instrument signals were assessed for stability by pumping temperature-controlled (±0.02 • C) water through the membrane [14].
x FOR PEER REVIEW 3 of 14 of dissolved gases across the membrane depends on the flow velocity and temperature and these parameters were held constant. All samples were measured at 20 °C. The gas stream was dried using a liquid nitrogen U-tube trap prior to entering the mass spectrometer. The instrument signals were assessed for stability by pumping temperature-controlled (±0.02 °C) water through the membrane [14].

Preparation of Standard Samples
CH4 standard samples were prepared using a headspace equilibrium method. A pressurized container containing 99.99% CH4, a sealed gas collecting bag, and a quantitative syringe were used to transfer CH4 to 12 mL Labco Exetainer vials. Before the addition, the vial volume was calibrated by weighing the water of a filled vial. After calibration, 7 mL of deionized water was added, leaving a 5 mL headspace. A known amount of CH4 was injected into the headspace through a quantitative gas-tight syringe. The vials were shaken for 5 min or more and then were put into a thermostatic water bath for solubility equilibration.

Measurement of Standard Samples
CH4 was conventionally measured with MIMS using mass 15, which was the CH3 + fragment of CH4, avoiding the pronounced and variable mass 16 peak that is associated with O + . This fragment was 90% of the intensity of the mass 16 peak of CH4 and sat on a low baseline peak. For nanomolar and low micromolar concentrations, it was necessary to use the secondary electron multiplier (SEM) detector.

Calculation of Dissolved CH4 in Standard Samples
The concentration of dissolved CH4 in standard samples was calculated according to Henry's law and Dalton's law. Henry's law was put forward by William Henry in 1803. It was applicable to the situation that there was no chemical reaction in the system and the temperature was constant. In this case, Henry's law states that the concentration of the gas dissolved in the liquid would be proportional to the partial pressure of the gas in the gaseous phase. Dalton's law states that for a gas mixture without a chemical reaction, the total pressure is equal to the sum of the partial pressures of all gases in the mixture. The specific formulas were as follows:

Preparation of Standard Samples
CH 4 standard samples were prepared using a headspace equilibrium method. A pressurized container containing 99.99% CH 4 , a sealed gas collecting bag, and a quantitative syringe were used to transfer CH 4 to 12 mL Labco Exetainer vials. Before the addition, the vial volume was calibrated by weighing the water of a filled vial. After calibration, 7 mL of deionized water was added, leaving a 5 mL headspace. A known amount of CH 4 was injected into the headspace through a quantitative gas-tight syringe. The vials were shaken for 5 min or more and then were put into a thermostatic water bath for solubility equilibration.

Measurement of Standard Samples
CH 4 was conventionally measured with MIMS using mass 15, which was the CH 3 + fragment of CH 4 , avoiding the pronounced and variable mass 16 peak that is associated with O + . This fragment was 90% of the intensity of the mass 16 peak of CH 4 and sat on a low baseline peak. For nanomolar and low micromolar concentrations, it was necessary to use the secondary electron multiplier (SEM) detector.

Calculation of Dissolved CH 4 in Standard Samples
The concentration of dissolved CH 4 in standard samples was calculated according to Henry's law and Dalton's law. Henry's law was put forward by William Henry in 1803. It was applicable to the situation that there was no chemical reaction in the system and the temperature was constant. In this case, Henry's law states that the concentration of the gas dissolved in the liquid would be proportional to the partial pressure of the gas in the gaseous phase. Dalton's law states that for a gas mixture without a chemical reaction, the total pressure is equal to the sum of the partial pressures of all gases in the mixture. The specific formulas were as follows: where H is the solubility coefficient of CH 4 (mol (L atm) −1 ), C CH 4 water is the CH 4 concentration in water (mol L −1 ), P CH 4 is the partial pressure of CH 4 in the headspace after reaching equilibrium. β is Benson's solubility coefficient. A 1 , A 2 , A 3 , B 1 , B 2 , and B 3 are constants and can be derived from previous studies [19]. S is the salinity of the solution (‰). T represents the water temperature (K). V m is the molar volume.
HS is the volume of CH 4 in the headspace after reaching equilibrium (L), VHS is the volume of headspace in the vial (L), P tot is the total pressure in the vial, P is the standard atmospheric pressure at 20 • C, and V CH 4 inj is the volume of the injection (L). Because the solubility of CH 4 is very low, changes in the total pressure due to the dissolution of CH 4 were ignored, indicating that the total pressure in the headspace was constant during the dissolution. V where V CH * 4 HS is the volume of CH 4 in the headspace before injection (L), V CH * 4 water is the volume of CH 4 in the water before injection (L), V CH * 4 HS is measured using GC, and V CH * 4 water is measured according to Equation (8):

Determination Range
We reviewed the concentrations of dissolved CH 4 in various natural waters. It can be seen from Table 1 that the concentrations of CH 4 in the natural water column were in the order of nanomolar to micromolar, which required our instrument to have a low detection limit. Therefore, the concentration of the CH 4 standard sample we prepared was within this range. Here, we configured eight CH 4 standard samples with different concentrations ranging from 2.63-593.93 nmol L −1 because previous studies showed that the concentration of CH 4 in freshwater Lake Taihu ranged from 0 to 400 nmol L −1 [20]. In order to demonstrate that our method was also applicable to saline aquatic ecosystems (such as oceans and saline lakes), we configured three CH 4 standard samples with different salinities (0, 15, and 30 respectively) [27], and established the CH 4 standard curves with MIMS. The method of standard sample preparation was the same as described above. The concentration of dissolved CH 4 in the standard sample was calculated according to Equation (8), where the specific concentrations are shown in Table 2.

Study Sites
Lake Taihu, which is one of the five largest freshwater lakes in China, is the largest lake in Jiangsu Province ( Figure 2a). The southern edge of the lake area is located on the boundary line between Jiangsu and Zhejiang provinces, with a lake area of 2340 km 2 . The annual average water depth is about 2 m, and the lake volume is 4.4 billion cubic meters [28]. Lake Taihu is located in a subtropical zone. The air temperature fluctuates between 3 and 37 • C. The annual average air temperature is 16.0-18.0 • C, and the annual precipitation is 1100-1150 mm. Farmland is the main land-use form surrounding Lake Taihu, accounting for 32.0%, followed by forest land, urban areas, and reservoirs and ponds, accounting for 27.6%, 18.7%, and 14.3%, respectively. The eutrophication of Lake Taihu was aggravated by human-induced nutrient loading. Due to the high degree of eutrophication in Lake Taihu, cyanobacteria have often bloomed during summer in recent years, which seriously affects the water quality [28][29][30][31][32]. Lake Taihu is a sink for nutrients and organic carbon [33] and is a large shallow lake with complex ecological types, including a planktonic algae zone (e.g., Dapu) (Figure 2d), aquatic plant zone (e.g., Xukou) (Figure 2c), and aquatic plant-algae transitional zone (e.g., Gonghu) [28]. These differences lead to the great spatial distribution of water quality and sediment properties. A recent study showed that there were also significant differences in CH 4 emissions from different regions of Lake Taihu. The CH 4 emissions in the algal and aquatic plant areas were significantly higher than that in other lake areas, and the CH 4 emission flux can reach 0.54 ± 0.30 g C m −2 yr −1 , which was seriously underestimated [8]. Thus, we took Lake Taihu as the study site and investigated the CH 4 concentration of surface water at 29 sites in all lake areas (Figure 2b). These 29 sampling sites were distributed evenly across the whole lake based on the lake area. The aim was to observe the differences between these areas and to evaluate the advantages and disadvantages of MIMS and GC in the measurement of dissolved CH 4 . In order to evaluate the method of MIMS regarding determining the CH 4 production capacities of sediments, we selected three different types of lake areas, namely, Dapu, Gonghu, and Xukou Bay, and collected undisturbed sediment columns at sites 9, 12, and 25 for laboratory experiments. The samples used for measuring CH 4 concentrations based on the MIMS method require to be preserved under non-headspace conditions. Therefore, we collected water samples from a depth about 20 cm below the water surface, because directly collecting samples from surface water may sample the ambient air and further affect the subsequent measurement. To compare with the MIMS method, the samples used for determining CH 4 concentrations based on the HGC method were also collected at the same depth, which was different from the traditional method that directly collected water samples at the water-air interface. Samples used for measuring CH 4 concentrations based on the MIMS method were immediately added with 100 μL saturated ZnCl 2 solution to inhibit microbial activity. Samples for the measurement of CH 4 concentration by the HGC method were prepared via equilibration with ambient air. Briefly, 400 mL surface water and 100 mL ambient air were sampled using a 2-way stopcock valve. With the valves closed, the bottle was shaken vigorously for about 5 minutes to reach equilibrium. The headspace was transferred to a serum bottle that was filled with saturated NaCl solution using two needles [34]. The gas samples were determined using a GC (Model Agilent GC6890N, Agilent Co., CA, USA) equipped with a flame ionization detector. It should be noted that the ambient air should be measured to adjust the dissolved gas headspace samples when comparing this method with the MIMS method. However, the ideal dissolved CH 4 concentration after balancing with the air above the surface water is very low (e.g., 3 nmol L -1 under 1.7 ppm in freshwaters in 20℃). Therefore, for waters with high CH 4 concentrations (e.g., Lake Taihu), the dissolved CH 4 in the water column was primarily from sediments and its self-production in water rather than from the atmosphere, indicating that CH 4 in

Method for Sampling and Data Acquisition
The samples that were used for measuring CH 4 concentrations based on the MIMS method needed to be preserved under non-headspace conditions. Therefore, we collected water samples from a depth about 20 cm below the water surface because directly collecting samples from surface water may sample the ambient air and further affect the subsequent measurement. To compare with the MIMS method, the samples used for determining the CH 4 concentrations based on the HGC method were also collected at the same depth, which was different from the traditional method that directly collected water samples at the water-air interface. The samples that were used for measuring CH 4 concentrations based on the MIMS method were immediately supplemented with 100 µL saturated ZnCl 2 solution to inhibit microbial activity. Samples for the measurement of CH 4 concentration using the HGC method were prepared via equilibration with ambient air. Briefly, 400 mL surface water and 100 mL ambient air were sampled using a 2-way stopcock valve. With the valves closed, the bottle was shaken vigorously for about 5 min to reach equilibrium. The headspace was transferred to a serum bottle that was filled with saturated NaCl solution using two needles [34]. The gas samples were determined using a GC (Model Agilent GC6890N, Agilent Co., CA, USA) that was equipped with a flame ionization detector. It should be noted that the ambient air should be measured to adjust the dissolved gas headspace samples when comparing this method with the MIMS method. However, the ideal dissolved CH 4 concentration after balancing with the air above the surface water is very low (e.g., 3 nmol L −1 under 1.7 ppm in freshwaters in 20 • C). Therefore, for waters with high CH 4 concentrations (e.g., Lake Taihu), the dissolved CH 4 in the water column was Water 2021, 13, 2699 7 of 14 primarily from sediments and its self-production in water rather than from the atmosphere, indicating that the CH 4 in the ambient air had little effect on the comparison between the MIMS method and the HGC method if we selected Lake Taihu (a large shallow lake with high CH 4 concentrations) as the sampling area. The water temperature at the sampling sites was measured using a multi-sensor probe (YSI 6600 V2).

Incubation Experiment for Sediment CH 4 Production
Rate CH 4 production rates from sediments were determined via incubation. A large sediment core was used to determine the denitrification and anammox rates based on the continuous flow-through method [35] in our previous studies [32]. Here, we also used a large core to collect sediment with the overlying water from the lake and then separated it into four smaller cores that were placed on the opposite end as the ejector pin ( Figure 3). These smaller cores were used to quantify the CH 4 flux at the sediment-water interface. The smaller cores were put into a constant temperature water bath where the temperature was set to the same as the lake water for incubation. Too long of an incubation time may lead to a decrease in the dissolved oxygen (DO) in the water column and may be unable to represent the in situ conditions; therefore, the incubation time was set at 2 days. The concentrations of CH 4 and DO were measured pre-incubation and post-incubation, respectively. Triplicate incubation experiments were conducted at the three sampling sites.
Water 2021, 13, x FOR PEER REVIEW 7 of 14 between the MIMS method and the HGC method if we selected Lake Taihu (a large shallow lake with high CH4 concentrations) as the sampling area. The water temperature at the sampling sites was measured using a multi-sensor probe (YSI 6600 V2).

Incubation Experiment for Sediment CH4 Production Rate
CH4 production rates from sediments were determined via incubation. A large sediment core was used to determine the denitrification and anammox rates based on the continuous flow-through method [35] in our previous studies [32]. Here, we also used a large core to collect sediment with the overlying water from the lake and then separated it into four smaller cores that were placed on the opposite end as the ejector pin ( Figure 3). These smaller cores were used to quantify the CH4 flux at the sediment-water interface. The smaller cores were put into a constant temperature water bath where the temperature was set to the same as the lake water for incubation. Too long of an incubation time may lead to a decrease in the dissolved oxygen (DO) in the water column and may be unable to represent the in situ conditions; therefore, the incubation time was set at 2 days. The concentrations of CH4 and DO were measured pre-incubation and post-incubation, respectively. Triplicate incubation experiments were conducted at the three sampling sites.

Calculation of CH4 Production Rates
The CH4 production rate was calculated using the concentration difference between post-incubation and pre-incubation. The calculation formula was as follows: where R is the CH4 production rate (μmol m −2 d −1 ), C0 is the initial CH4 concentration (μmol L −1 ), C is the CH4 concentration after incubation (μmol L −1 ), V is the headspace volume (L), S is the basal area of the incubation column (m 2 ), and T is the incubation time (day).

Comparison with GC Method
We used GC to measure the concentration of CH4 in the headspace to calculate the concentration of dissolved CH4 in the samples. The specific calculation formula was as follows:

Calculation of CH 4 Production Rates
The CH 4 production rate was calculated using the concentration difference between post-incubation and pre-incubation. The calculation formula was as follows: where R is the CH 4 production rate (µmol m −2 d −1 ), C 0 is the initial CH 4 concentration (µmol L −1 ), C is the CH 4 concentration after incubation (µmol L −1 ), V is the headspace volume (L), S is the basal area of the incubation column (m 2 ), and T is the incubation time (day).

Comparison with GC Method
We used GC to measure the concentration of CH 4 in the headspace to calculate the concentration of dissolved CH 4 in the samples. The specific calculation formula was as follows: C water represents the methane content in the water before equilibrium (µmol L −1 ), C CH 4 HS is the CH 4 content in the headspace after equilibrium (µmol L −1 ), H is Henry's law constant (mol (L atm) −1 ), R is the ideal gas constant (L atm (mol K) −1 ), T is the temperature (K), V HS is the volume of headspace (L), and V water is the volume of water (L).

Statistical Analysis
Linear regression was usually used to detect the relationship between two variables. Here, we used linear regression to show the relationship between the dissolved CH 4 concentration and the CH 4 signal value from MIMS to test whether the MIMS method was reliable. Linear regression was also used to investigate the relationship between dissolved CH 4 concentrations derived from the two different methods. Furthermore, we used the t-test to show the differences in the dissolved CH 4 concentrations derived from the two different methods. If the p-value was greater than 0.05, it indicated no significant differences in the dissolved CH 4 concentrations derived from the two different methods. The linear regression was performed using Origin 8.0, while the t-test was conducted using IBM SPSS 19.0. The figures were produced in Origin 8.0 and ArcGis 10.4.1.

Instrument Response to CH 4 Standards
The standard curves across a range of air saturation (1.7 nM) to 800 µM were highly linear (R 2 > 0.999; Figure 4b). In addition, under three different salinities, the relationship (Figure 4a) between the CH 4 concentration and signal value were very significant (R 2 = 0.99813, p < 0.0001 for S = 0; R 2 = 0.99733, p < 0.0001 for S = 15; R 2 = 0.99882, p < 0.0001 for S = 30), indicating that salinity had little effect on the accuracy of standard curves. where C represents the methane content in the water before equilibrium (μmol L −1 ), C is the CH4 content in the headspace after equilibrium (μmol L −1 ), H is Henry's law constant (mol (L atm) −1 ), R is the ideal gas constant (L atm (mol K) −1 ), T is the temperature (K), VHS is the volume of headspace (L), and Vwater is the volume of water (L).

Statistical Analysis
Linear regression was usually used to detect the relationship between two variables. Here, we used linear regression to show the relationship between the dissolved CH4 concentration and the CH4 signal value from MIMS to test whether the MIMS method was reliable. Linear regression was also used to investigate the relationship between dissolved CH4 concentrations derived from the two different methods. Furthermore, we used the ttest to show the differences in the dissolved CH4 concentrations derived from the two different methods. If the p-value was greater than 0.05, it indicated no significant differences in the dissolved CH4 concentrations derived from the two different methods. The linear regression was performed using Origin 8.0, while the t-test was conducted using IBM SPSS 19.0. The figures were produced in Origin 8.0 and ArcGis 10.4.1.

Instrument Response to CH4 Standards
The standard curves across a range of air saturation (1.7 nM) to 800 μM were highly linear (R 2 > 0.999; Figure 4b). In addition, under three different salinities, the relationship (Figure 4a) between the CH4 concentration and signal value were very significant (R 2 = 0.99813, p < 0.0001 for S = 0; R 2 = 0.99733, p < 0.0001 for S = 15; R 2 = 0.99882, p < 0.0001 for S = 30), indicating that salinity had little effect on the accuracy of standard curves.

Comparison of the MIMS and HGC Methods
In order to determine whether MIMS was reliable, we compared the results with HGC measurements. We selected 29 sites in Lake Taihu and determined the concentration of CH4 in the surface water using HGC and MIMS. As shown in Figure 5a, the spatial distribution of CH4 concentrations in the surface water of Lake Taihu was greatly significant, ranging from 0.02 to 0.70 μmol L −1 based on the MIMS method. As a whole, the values obtained from MIMS were consistent with those from HGC, and the linear relationship was also very significant (Figure 5b). Interestingly, we observed that the slope of the fitting curve was greater than 1 and the CH4 concentrations derived from the MIMS method in many sampling sites were a bit higher than those derived from the HGC method; however, this difference was not significant according to the t-test (p > 0.05).

Comparison of the MIMS and HGC Methods
In order to determine whether MIMS was reliable, we compared the results with HGC measurements. We selected 29 sites in Lake Taihu and determined the concentration of CH 4 in the surface water using HGC and MIMS. As shown in Figure 5a, the spatial distribution of CH 4 concentrations in the surface water of Lake Taihu was greatly significant, ranging from 0.02 to 0.70 µmol L −1 based on the MIMS method. As a whole, the values obtained from MIMS were consistent with those from HGC, and the linear relationship was also very significant (Figure 5b). Interestingly, we observed that the slope of the fitting curve was greater than 1 and the CH 4 concentrations derived from the MIMS method in many sampling sites were a bit higher than those derived from the HGC method; however, this difference was not significant according to the t-test (p > 0.05).

CH4 Concentrations and Sediment CH4 Production Rates in Lake Taihu
In Xukou Bay, the concentrations of CH4 in surface water were very high, where the highest value was more than 0.63 μmol L −1 (Figure 5a), but it was very low in the center of the lake, which was less than 0.1 μmol L −1 in some sites. We used MIMS to determine the concentration of dissolved CH4 in a non-headspace incubation experiment, where the results are shown in Figure 6. The dissolved CH4 accumulations were observed in the cores of Xukou, Dapu, and Gonghu Bays (Figure 6a). The CH4 production rate in Xukou Bay was the highest, reaching 0.48 ± 0.34 mmol m −2 d −1 , followed by Gonghu and Dapu Bays, with the values of 0.19 ± 0.04 and 0.12 ± 0.06 mmol m −2 d −1 , respectively (Figure 6b). These results indicated that the CH4 production was obvious in these three sampling sites. Generally, no significant decrease in DO concentrations was observed during the incubation experiment.

CH 4 Concentrations and Sediment CH 4 Production Rates in Lake Taihu
In Xukou Bay, the concentrations of CH 4 in surface water were very high, where the highest value was more than 0.63 µmol L −1 (Figure 5a), but it was very low in the center of the lake, which was less than 0.1 µmol L −1 in some sites. We used MIMS to determine the concentration of dissolved CH 4 in a non-headspace incubation experiment, where the results are shown in Figure 6. The dissolved CH 4 accumulations were observed in the cores of Xukou, Dapu, and Gonghu Bays (Figure 6a). The CH 4 production rate in Xukou Bay was the highest, reaching 0.48 ± 0.34 mmol m −2 d −1 , followed by Gonghu and Dapu Bays, with the values of 0.19 ± 0.04 and 0.12 ± 0.06 mmol m −2 d −1 , respectively ( Figure  6b). These results indicated that the CH 4 production was obvious in these three sampling sites. Generally, no significant decrease in DO concentrations was observed during the incubation experiment.

CH4 Concentrations and Sediment CH4 Production Rates in Lake Taihu
In Xukou Bay, the concentrations of CH4 in surface water were very high, where the highest value was more than 0.63 μmol L −1 (Figure 5a), but it was very low in the center of the lake, which was less than 0.1 μmol L −1 in some sites. We used MIMS to determine the concentration of dissolved CH4 in a non-headspace incubation experiment, where the results are shown in Figure 6. The dissolved CH4 accumulations were observed in the cores of Xukou, Dapu, and Gonghu Bays (Figure 6a). The CH4 production rate in Xukou Bay was the highest, reaching 0.48 ± 0.34 mmol m −2 d −1 , followed by Gonghu and Dapu Bays, with the values of 0.19 ± 0.04 and 0.12 ± 0.06 mmol m −2 d −1 , respectively (Figure 6b). These results indicated that the CH4 production was obvious in these three sampling sites. Generally, no significant decrease in DO concentrations was observed during the incubation experiment.

Assessment of the Analytical Technique
CH 4 detection using MIMS has a 40-year history, where it has been primarily used for microbiological rate measurements under experimental conditions [12]. MIMS has not been the preferred method for environmental water samples; instead, the HGC method is commonplace. Notably, submersible MIMS is incorporated in ROVs for sniffing hydrocarbons in marine systems [36]. Here, we describe a MIMS method that is rapid, precise, sensitive, suited to both trace and highly concentrated samples, and suited to the environmental sampling of water bodies. Contributing to these characteristics is the configuration of the membrane interface. The MIMS used in this study constrains diffusion by imposing a laminar flow across the membrane and having good temperature control of the water flowing across the membrane. This results in sample replicate C.V.s of 0.2% for ion currents (proportional to concentration data) and 0.03% for gas ratios for air gases [14]. CH 4 detection at mass 15 avoids interference from variable O 2 in environmental water samples. However, depending on the mass spectrometer and its settings, there can be mass overlap across adjacent unit masses [37,38]. In the case of CH 4 , the mass spectrometer mass resolution may allow O + ions to be detected at mass 15. This can have a significant effect that is observed as a correlation between mass 15 ion currents and oxygen concentration when measuring trace levels of CH 4 . The effect can be minimized or eliminated by reducing the resolution parameter of the quadrupole mass spectrometer. Mass 15 is the methyl ion that is also produced by the fragmentation of organic molecules that may pass through the membrane. The use of a liquid nitrogen cryotrap in this study effectively traps all organics that may otherwise interfere at mass 15. Therefore, the mass 15 signal represents an unambiguous measure of CH 4 using the MIMS configuration described here. We demonstrated linearity across low nanomolar to high micromolar concentrations spanning the range expected in nature, including systems experiencing CH 4 ebullition.

Comparison with HGC
As shown in Figure 5b, the linear relationship between the dissolved CH 4 concentrations derived from the two different methods was significant. However, there were still some small differences. We are confident in the MIMS method because of the satisfactory standard curves (Figure 4). Hence, we speculated that these small differences may have been caused by the potential errors in the HGC method. Headspace equilibration was used to prepare the standard samples for determining CH 4 concentrations using the MIMS method. During the standard sample preparation, the vials were shaken for more than 5 min, which was the same as collecting water samples using the HGC method during the field sampling. The standard curves show that the CH 4 signal values displayed very close relationships for various CH 4 concentrations. Hence, we concluded that the small differences in CH 4 concentrations may not have been caused by incomplete equilibration. Here, we speculated that this small difference may have been due to the following reasons: (1) In the traditional HGC method, the saturated NaCl solution was replaced by the headspace that was from the syringe after the equilibration with lake water. This process was conducted using two gas-tight syringes. However, the injection of the headspace into the serum bottle that was filled with saturated NaCl solution may have easily cause micro-bubbles. Such micro-bubbles may escape with the NaCl solution through another syringe, leading to an underestimate of the dissolved CH 4 concentrations. Furthermore, the higher the CH 4 in the headspace, the higher the underestimate of the dissolved CH 4 concentration will be. (2) Some CH 4 in the headspace may redissolve in the NaCl solution. For a high CH 4 concentration in the headspace, the loss of CH 4 in the headspace caused by redissolution is also high, which may be one of the important reasons for the higher dissolved CH 4 obtained from the MIMS method under high CH 4 concentrations. (3) The transfer of headspace from the syringe to the serum bottle should be conducted carefully. However, during the field samplings, there are too many factors that may affect the transfer, such as the shaking of the boat induced by lake waves due to a high wind speed. Such shaking often appears in large, shallow, and open waters (e.g., Lake Taihu).
In the MIMS method, in addition to the standard samples, the collected field samples do not need headspace processing, and the sampling device is very simple. Only a 12 mL water sample is needed at each site for determination, which means that we can take multiple samples for analysis to reduce the systematic error. It takes about 5 min to determine a sample using the HGC method, but less than 2 min for the MIMS method, which greatly improves the efficiency of sample determination. In addition, the MIMS method can simultaneously measure oxygen, nitrogen, and argon from the same sample vial, which saves a lot of time and labor costs. Furthermore, during the field sampling, the HGC method requires shaking the lake water with air for at least 5 min, while using the MIMS method does not need to make a headspace during sampling and the sampling can be finished within 30 s. For large waters, such as Lake Taihu, sampling from 29 sites across the whole lake using the MIMS method can be finished within half a day. However, it would take at least 2 days if we used the HGC methods. As is well known, the temporal change may lead to the variation in CH 4 concentrations. Therefore, for those who want to collect numerous samples on a short-time scale or want to investigate the spatial distribution of CH 4 concentrations in waters, the MIMS method is more preferred. Additionally, due to the rapid response of the MIMS signal to the variation in CH 4 concentration, MIMS can be used for real-time monitoring of the concentration of CH 4 if desired, which cannot be achieved using the HGC method. It should be noted that the MIMS method also has limitations. Compared with the HGC method, the MIMS method cannot be used to simultaneously determine the concentrations of dissolved carbon dioxide and nitrous oxide since these two gases have almost the same relative atomic mass (~44), which can not be distinguished using MIMS.

Assessment of the MIMS Method in Lake Taihu
The peak value of the CH 4 concentration measured using the MIMS method appeared in Xukou Bay (Figure 5a), which may have been related to the large number of floating plants and submerged plants there. The degradation of aquatic plants will add a lot of organic carbon to the water and sediments, which is the substrate of CH 4 production [39]. The incubation experiment indicated that Lake Taihu was an important source of CH 4 in summer. A study has shown that submerged macrophytes can significantly promote CH 4 emission from lakes. In our experiment, the CH 4 production rate of sediments in Xukou Bay was the highest, which may be related to the large number of aquatic plants and submerged plants there. Evident CH 4 accumulations also appeared in Dapu and Gonghu Bays. These two lake areas were covered with algae, and the presence of cyanobacteria could significantly promote CH 4 production [40]. Here, we compared our results with those in previous studies, where the results are shown in Table 3. Our results were generally lower than those in previous studies, which may have been related to the different properties of sediments; however, the rate of CH 4 release from sediments into the water column was still very high, suggesting that shallow waters (e.g., Lake Taihu) were hotspots for CH 4 production and emission.

Conclusions
In this study, we introduced a novel method based upon the MIMS method to determine the dissolved CH 4 concentrations in natural waters. This method was tested in the laboratory and further applied to a large shallow lake, namely, Lake Taihu. Water samples, as well as sediment cores, were collected from Lake Taihu in the summer of 2020 to quantify the CH 4 concentration and CH 4 production rates based on the MIMS method. The results showed that Lake Taihu was an important source of CH 4 in summer. Furthermore, a comparison between the MIMS method with the traditional method (HGC method) was also conducted. Laboratory tests and field sampling showed that our method had significant advantages when measuring dissolved CH 4 , including high precision, simple pretreatment, and a fast response. In addition, our method is not only suitable for freshwater lakes, but also other high salinity aquatic ecosystems, such as oceans and saline lakes. We are confident that our MIMS method can replace the traditional HGC method for the determination of dissolved CH 4 . Through our method, we could accurately quantify the water-air diffusive flux of CH 4 and determine the CH 4 release rate from sediments to the water column, which provides great convenience regarding studying the fate of CH 4 .