Using Automated Eddy-covariance Stations for ...

Air Quality Measurement Methods and Technology, March 2016

Using Automated Eddy-covariance Stations for Studying Landfill Methane Emissions G. Burba1, D. McDermitt1, L. Xu1, J. Li1, R. Green2, J. Chanton3, K. Welding4; 1

LI-COR Biosciences, Lincoln, NE, 2Waste Management, Cincinnati, OH, 3Department of Earth, Ocean & Atmospheric Science, Florida State University Tallahassee, FL, 4Bluff Road Landfill, Lincoln, NE

Introduction Long-term continuous and quantitative understanding of methane emission from landfills and how environmental variables control the emission are essential for modeling studies and determining the mitigation strategy to control methane emissions. In this paper we report continuous methane emission studies over two landfills using the eddy covariance method. One, Bluff Road Landfill, is near the city of Lincoln in Nebraska. The other, Turkey Run Landfill, is located in northern Meriwether County, Georgia. The main objectives of our study are: (1) to investigate whether the eddy-covariance method can be used to quantify landfill methane emission; (2) to understand the impact of changes in barometric pressure on landfill methane emissions; (3) to test a simple stoichiometric model we developed recently for estimating landfill methane oxidation fraction using eddy-covariance CO2 and CH4 flux data.

Material and Methods Site Information Bluff Road Landfill is located north of Lincoln, Nebraska (40.908oN, 96.638oW, 367 m above sea level), which is just outside the city limit. The landfill opened in October, 1988, and is due for closure around the year 2035. It covers approximately 69 hectares, with a capped area of 16 ha. The total capacity of the landfill is 23.6 million tons. By the end of October 2010, the estimated total amount of waste already in place was 6.1 million tons. The instrument station was located in the middle of a relatively flat plateau of the landfill. The north half section of the landfill was capped with a geomembrane liner and a 0.5-m layer of clay. The landfill gas diffuses out passively to the atmosphere through evenly distributed vents. On average, there was one vent per 0.3 hectares. The south half of the landfill was capped only with a 0.5-m layer of clay, no geomembrane liner 1

was installed at the time, allowing the landfill gas to diffuse out through the clay layer. Based on its design drawing, the waste depth at the capped area ranges from 18 to 40 m. Additional detail regarding this site are provided in Xu et al. (2014). Turkey Run Landfill is located in northern Meriwether County, Georgia (33.174oN, 84.848oW, 243 m above sea level). The landfill covers 20 hectares and started collecting waste since 2009. Waste was placed first at east, south side, and southwest sides. At north side, the placing of waste was on-going during our field experiment. The landfill was capped with a 0.5-m layer of clay without having a geomembrane liner. Additional detail regarding this site are provided in Li et al. (2015). Eddy covariance method The eddy covariance flux measurement at Bluff Road Landfill has been running since June 1, 2010, and the data reported in this paper were obtained from June 2010 to Dec 2010. The measurement at Turkey Run Landfill started on April 25, 2012 and continued until May 8, 2013. The eddy-covariance method is a micrometeorological method using the theory of turbulent transport in the surface layer of the atmosphere [Verma et al., 1986; Baldocchi et al., 1988; Burba, 2013]. It estimates a particular gas flux from the covariance between vertical wind speed and the gas concentration measured at some carefully chosen height above a surface. Typically, vertical wind speed and gas concentration are both measured at 10 Hz and their covariance is calculated normally with 30 min intervals (Equation 1). With the eddy covariance method, methane emission rate (FCH4) can be calculated using the following covariance equation: 𝐹𝐶𝐻4 = ̅̅̅̅̅̅̅̅̅̅ 𝑤′𝜌𝐶𝐻4 ′

(1)

where w’ is the deviation of vertical wind velocity from its 30 min mean (m s-1), CH4’ is the deviation of methane number density from its 30 min mean (mmol m-3). The overbars indicate the 30-min average based on 10 Hz sampling rate data.

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Figure 1. Setup of the eddy covariance flux instrumentation at Bluff Road Landfill, Lincoln Nebraska. Instruments shown include an open-path CH4 analyzer, a 3-D sonic anemometer, and an open-path CO2/H2O analyzer. Solar panels were used to power all of the instruments at this site. A radio link (not shown) was used for data transmission and for instrument control via internet.

Eddy covariance flux instruments used at both study sites included an open-path CO2/H2O gas analyzer (Model LI-7500A, LI-COR Biosciences, Lincoln, NE, USA), an open-path CH4 gas analyzer (Model LI-7700, LI-COR Biosciences, Lincoln, NE, USA), a sonic anemometer (Gill Windmaster Pro, Model 1352, Gill Instruments Ltd., Lymington, England), solar power system, communication etc. The gas analyzers and sonic anemometer were installed at the height of 3 m at Bluff Road Landfill (Fig. 1) and 2.36 m at Turkey Run Landfill. The barometric pressure was measured with a pressure transducer (model 1800-03A-L3N-B, Honeywell, Freeport, Illinois, USA) in the open-path CH4 analyzer. According to the manufacturer’s specification sheet, the transducer has an accuracy of ±12.9 Pa and a response time of 1 ms. The main advantages of the eddy covariance method over others are: (1) it provides an in situ and direct measurement of spatially averaged gas emission over a large area in the upwind direction (normally to a distance of 100 times the instrument height), (2) it has the capability of automation for continuous measurements, (3) it leaves the surface undisturbed, (4) limited maintenance is required. The Stoichiometric Model: When methane generated under anaerobic zone inside a landfill passes through the top cover soil, fraction of the methane will be oxidized due to the presence of oxygen and methanotrophic bacteria. One of the uncertainties in modeling landfill methane emissions is the methane oxidation fraction. We developed a simple stoichiometric model to estimate this fraction using the information of landfill CO2 and CH4 flux and the anaerobic CO2 / CH4 production ratio.

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Figure 2. An illustration showing the three sources of landfill CO2 emission (FCO2): anaerobic production (CO2), production of CO2 from oxidation of methane (xCO2), and aerobic production at the surface layer (SCO2). The methane emission (FCH4) is anaerobic production (CH4) minus the oxidation loss (xCH4).

Before we show the derivation of the model, we first define the following variables. FCO2: flux of CO2 from a landfill surface (mol m-2s-1) FCH4: flux of CH4 from the landfill surface (mol m-2s-1) CO2: anaerobic production rate of CO2 (mol m-2s-1) CH4: anaerobic production rate of CH4 (mol m-2s-1) xCO2: aerobic production rate of CO2 due to oxidation of methane (mol m-2s-1) SCO2: aerobic production rate of CO2 due to direct oxidation of organic matter (mol m-2s-1) xCH4: oxidation rate of methane (mol m-2s-1) β: fraction of methane oxidized (dimensionless) r: molar ratio of anaerobic CO2 produced to anaerobic CH4 produced (0.82, ratio of CO2 concentration to CH4 concentration from the gas sample taken from anaerobic zone). Under a steady state, the CO2 flux at the landfill surface is the sum of anaerobic CO2 production (CO2), the amount of CO2 coming from oxidation of methane (xCO2), aerobic CO2 production (SCO2): 𝐹𝐶𝑂 2 = 𝑎𝐶𝑂2 + 𝑥𝐶𝑂2 + 𝑆𝐶𝑂2 , (2) 𝐹𝐶𝐻 4 = 𝑎𝐶𝐻4 − 𝑥𝐶𝐻4 ,

(3)

|𝑥𝐶𝑂2 | = |𝑥𝐶𝐻4 | = |𝛽𝑎𝐶𝐻4 |

(4)

So, from equations (3) and (4): 𝐹𝐶𝐻 4 = 𝑎𝐶𝐻4 − 𝛽𝑎𝐶𝐻4 , 𝐹𝐶𝐻 4 = 𝑎𝐶𝐻4 (1 − 𝛽), 𝐹

𝐶𝐻 4 And then: 𝑎𝐶𝐻4 = (1−𝛽) .

Let

𝑎𝐶𝑂2

𝑟=𝑎

𝐶𝐻4

(5)

,

(6) 4

𝑎𝐶𝑂2 = 𝑟𝑎𝐶𝐻4 .

So

(7)

Therefore, from (2), (4) and (7): 𝐹𝐶𝑂 2 = 𝑎𝐶𝑂2 + 𝑥𝐶𝑂2 + 𝑆𝐶𝑂2 , 𝐹𝐶𝑂 2 = 𝑟𝑎𝐶𝐻4 + 𝛽𝑎𝐶𝐻4 + 𝑆𝐶𝑂2 , And 𝐹𝐶𝑂 2 = 𝑎𝐶𝐻4 (𝑟 + 𝛽) + 𝑆𝐶𝑂2 .

(8)

Also, from (5) and (8), we have: 𝑟+𝛽

𝐹𝐶𝑂 2 = (1−𝛽) 𝐹𝐶𝐻 4 + 𝑆𝐶𝑂2

(9)

So, the methane oxidation fraction () can be estimated based on the slope of the linear regression when FCO2 is plotted against FCH4.

Results

Methane emission rate (mol m-2s-1)

Using the eddy covariance method to quantify the landfill methane emission 100 80

0.5 hr 1-day mean 10-day mean

60 40 20 0 06/01/10

07/01/10

08/01/10

09/01/10

10/01/10

11/01/10

12/01/10

01/01/11

Date (mm/dd/yy)

Figure 3. Seasonal variations in hourly methane emission rate (open black circles), 1-day mean (solid blue line), and 10-day mean (solid red line) methane emission rate over the experiment period. The mean methane emission over the entire experiment was 17.7 mol m-2s-1.

Hourly emission data from Bluff Road Landfill are shown in Figure 3. The emission rates varied widely throughout the duration. In the warm season, they varied from almost zero to over 50 mol m-2s-1. However, in the cold season, even larger variations from zero to around 100 mol m-2s-1 were observed (Figure 3). Note that the maximum hourly emission rate in the cold season nearly doubled as compared to that in the warm season. 5

When we averaged hourly methane emission rates into a daily mean, a large day-to-day variation could be easily seen (Figure 3). For example, the daily mean on September 11 was 6.4 mol m-2 s-1. The next day on September 12, the mean increased to 26.4 mol m-2s-1, a 4.1-fold increase. Like the hourly emission rate, the variation of daily mean emission was larger in the cold season than that in the warm season. For an example, the daily mean emission rate on December 21 was only 1.8 mol m-2s-1. On the next day (December 22) the daily mean rate was 63.8 mol m-2s-1, a 35.6-fold increase explained in the following sections. When we averaged the hourly emission rate into 10-day means, little variation can be seen in the data in the warm season (Figure 3). The hourly and daily methane emission variation likely were due to the impact of changing in barometric pressure on landfill methane emission as we will illustrate below. The mean methane emission from Bluff Road Landfill over the half year was 17.7 mol m-2s-1. This mean value is well within the range of methane emission rates reported from earlier studies [Lohila et al., 2007; Goldsmith et al., 2012]. This seems to suggest that the methane emission measured with the eddy covariance method at Bluff Road Landfill was dominated by emissions from the landfill and was not substantially affected by the emission from the surrounding landscape. Also from Figure 3, the 10-day mean methane emission is fairly stable over the course of our experiment. This phenomenon of stable emission has been reported in the literature and has been attributed to the relatively stable temperature inside the landfill over the season (Chanton and Liptay, 2000; Lohila et al., 2007). Our measured methane emission rate and seasonal variation seems to suggest that the eddy covariance can be used to measure landfill methane emission as long as certain requirements (relative flat, enough fetch) are met. Response of landfill methane emission to changes in barometric pressure Figure 4 illustrates how quickly the atmospheric methane concentration measured at Bluff Road Landfill responds to changes in the barometric pressure. Both the methane concentration and the barometric pressure were measured with the open-path methane analyzer at the height of 3 m. The dataset was obtained on June 7, 2010 during the passage of a cold front. The barometric pressure started increasing at 13:27. Three minutes later, the methane concentration dropped from 50 ppm to 7 ppm (v/v, parts per million). As the pressure continued to increase, methane concentration further decreased to the atmospheric background level of about 2 ppm by 13:32. Note that for this event the barometric pressure increased from 96.95 kPa at 13:27 to 97.13 kPa at 13:37, about 0.18kPa increase in 10 min, a change rate of 1.08 kPa hr-1. This was a relatively high rate, as the rates of pressure change we normally saw during the half-year experiment period were in the range of ±0.1 kPa hr-1. We also note that the large variations in methane concentration before 13:30 were due to vertical wind fluctuations. The open-path methane analyzer most likely would capture

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higher concentrations of methane when the air was moving upward and lower concentrations when the air was moving downward.

97.15

50 40

97.10 Pressure

CH4

97.05

30 97.00 20 96.95

10 0 13:20

96.90 13:25

13:30

13:35

Barometric pressure (kPa)

CH4 concentration (ppm)

60

Figure 4. The response of atmospheric methane concentration (open dark symbols) to the increase in barometric pressure (black dotted line). This dataset was obtained on June 7, 2010 at Bluff Road Landfill during the passage of a cold front. Both the methane concentration and the barometric pressure were measured with the open-path methane analyzer at the height of 3 m.

Time (of Jun 7, 2010)

An example of the response of the methane emission rate to changes in barometric pressure is shown in Figure 5. The dataset was obtained at Bluff Road Landfill from September and early October (Sept. 8 to Oct. 3). It is clear from Figure 5 that whenever barometric pressure was rising (solid line boxes), the emission rate was greatly suppressed, and whenever barometric pressure was falling (dashed line boxes), the emission rate was greatly increased. For example, from Sept. 8 at 14:00 to Sept. 10 at 21:00 when atmospheric pressure was steadily falling from 97.234 kPa to 95.882 kPa, the average methane emission during this period was 31.1 mol m-2s-1. Immediately after this pressure drop, a cold front moved into the area. The pressure rose from 95.882 kPa on Sept. 10 at 21:00 to 96.972 kPa on Sept 11 at 18:30, the average emission rate was suppressed to as low as 5.1 mol m-2s-1, only one sixth of that from the pressure falling phase. The same phenomena occurred repeatedly throughout the rest of our field experiment. The strong dependence of landfill methane emission on the changes in barometric pressure is not totally new. The relationship between methane emission rate and changes in barometric pressure over landfills (Young, 1990; Czepiel et al., 2003; Poulsen et al., 2003) and wetlands (Mattson and Likens, 1990; Shurpali et al., 1993; Tokida et al., 2007) has been observed in many studies. In addition, this relationship has also been known to mining ventilation engineers in the United Kingdom for more than 250 years (McQuaid and Mercer, 1991). In fact, some mining explosions in the United Kingdom have been linked to low atmospheric pressure weather systems. According to McQuaid and Mercer (1991), if barometric pressure falls too quickly, mining operations need to be suspended regardless of whether or not a modern ventilation systems is in use, and not resumed until barometric pressure starts increasing.

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100

100 CH4 emission

99

Pressure

80

98

60

97

40

96

20

95

0

94

-20

9/8/10

9/13/10

9/18/10

9/23/10

9/28/10

Pressure (kPa)

CH4 emission (mol m-2s-1)

120

93 10/3/10

Date (mm/dd/yy)

Figure 5: Time series of hourly methane flux (closed grey symbol) and barometric pressure (closed black symbol) at landfill during September and early October 2010. Solid line boxes represent phases when pressure is rising, and dashed line boxes represent phases when pressure is falling. Since the production of methane inside the landfill is relatively stable over the course of a year (Chanton and Liptay, 2000; Lohila et al., 2007), the sensitivity of methane emission to the changes in barometric pressure most likely is from changes in the pool size, i.e. via changes in methane storage inside the landfill. During the pressure rising phase, a layer of fresh ambient air was continuously pushed into the landfill, making it very difficult for CH4 to diffuse out. While during the pressure falling phase, the top layer of air inside the landfill was flushed out, increasing methane emission. In the meantime, stripping away the top layer of the air would also increase the CH4 concentration diffusion gradient between the atmosphere and inside the landfill, further enhancing methane emission. We have shown that methane emissions at the Bluff Road landfill near Lincoln, NE responded dynamically to changes in barometric pressure (Figure 4 and 5). It is reasonable to expect that responses of landfill methane emissions to barometric pressure variations in other parts of the world would be similar to what we observed in this present study. So our result has an important implication. Point-in-time methane emission measurements made at monthly or even longer time intervals with techniques such as the trace plume method, mass balance method, or closed-chamber method may be subject to large variations in measured emission rates, because the measured methane emissions would strongly depend on the changes in barometric pressure. Estimates of long term integrated total landfill methane emissions based on such measurements likely will have large uncertainties. Our results demonstrate that continuous measurements greatly improve the likelihood of accurately estimating annual total landfill methane emissions.

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Test the stoichiometric model for estimating landfill methane oxidation fraction We use the CO2 and CH4 emission data to test the stoichiometric model to estimate the landfill methane oxidation fraction. When we plot FCH4 against FCO2 from eddy covariance measurements, 𝑟+𝛽 the slope from the linear regression will tell us the value of 1−𝛽, and the offset will be SCO2, which

1/13/2013

4/18/2013

30

-2 -1

30

FCO2 (mol m s )

FCO2 (mol m-2s-1)

is the soil respiration from cover soil plus direct oxidative respiration of waste material. At Turkey Run landfill, we take r as 0.82, the ratio of CO2 concentration (45%) to CH4 concentration (55%) from the gas sample taken from deep inside the landfill, assuming that both CO2 and CH4 is all coming from anaerobic production. Two examples are shown in Figure 6 with the emission data obtained on Jan 13, 2013 and Apr 18, 2013. With the information of linear regression slope of 1.297 and 1.583, we estimate the oxidation fraction to beandfor these two days.

20

20

10

10 Y=1.297X+2.812 R2=0.985

Y=1.583X+1.395 R2=0.823

0 0

5

10

15

0

5

10

15

0 20

FCH4 (mol m-2s-1)

Figure 6. Two examples (Jan 13, 2013 and Apr 18, 2013) of linear relationship between landfill CO2 flux (FCO2) and CH4 flux (FCH4). Wind direction during these two days ranged from 120-180°. Data were obtained from Turkey Run Landfill. We found that the linear relationship between CO2 and CH4 flux depends on the wind direction at Turkey Run landfill. An example is shown in Figure 7 with data obtained from Feb. 17 to 18, in 2013. We can see that there is a good linear relationship when the wind came from 80-180° with the estimated oxidation fraction of 18.3%. However, the relationship broke down when the wind came from northwest (250-350°). We consistently observed that emissions from the northwest direction where new waste was being placed produced relatively higher FCO2 and lower FCH4 and regressions had higher intercepts, generally steeper slopes, and more variability. Thus, at locations with newer deposition, the landfill may not be fully anaerobic, with consequent higher direct oxidation of the waste, higher oxidation of methane produced, and more site-to-site variability.

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2/17- 18/2013

40

-2 -1

FCO2 (mol m s )

Figure 7: The dependence of linear relationship between CO2 flux (FCO2) and CH4 flux (FCH4) on wind direction. Data were obtained on Feb 17-18, 2013 from Turkey Run Landfill.

Y=1.227X+1.776 R2=0.98

30

20

10

Wind from 80-180o Wind from 250-350o Linear regression

0 0

5

10

15

20

25

-2 -1

FCH4 (mol m s )

Table 1 shows the landfill methane oxidation fraction estimated using the stoichiometric method for different days during the year of 2012 to 2013 and the comparison with the oxidation fraction using isotopic method based on the gas samples collected at Turkey Run Landfill. See Liptay and Chanton (1998) for the detail of the isotopic method. The comparison is reasonably close. The difference most likely is due to the different footprint represented by these two methods. We know that the footprint for the stoichiometric method could represent the average area in the upwind direction normally to a distance of 100-200 meters, while for the isotopic method, its footprint is likely to be much smaller.

Conclusion Our results show that the eddy covariance can be used to quantify the landfill methane emission as long as certain requirements, relatively flat surface and large enough fetch, are met. Our results show that the methane emission rates at the landfill strongly depend on changes in barometric pressure; i.e., rising barometric pressure suppresses the emission, while falling barometric pressure enhances the emission (Figure. 5). There was up to 6-fold variation of methane emissions from day-to-day due to changes in barometric pressure. Table 1. Comparison of landfill methane oxidation estimated with the Stoichiometric model and using stable isotopic analysis.

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Date 4/25/2012 6/28/2012 12/5/2012 3/7/2013 4/11/2013 5/8/2013

CH4 Oxidation Fraction () Isotopic Method*

Stoichiometric Method

0.26 0.45 0.36 0.29 0.21 0.44

0.45 0.33 0.54 n/a 0.21 0.36

Remark Flux data were from 4/26/2012 Flux data were from 12/4/2012 and 12/5/2012 Wind from north Flux data were from 5/7/2013

* See Liptay and Chanton (1998) for the detail of the isotopic method. Our results also show that emission measurements taken at monthly or even longer time intervals using techniques such as trace plume method, mass balance method, or the closed-chamber method should be expected to have a large variation in measured rates because of the strong dependence of methane emissions on changes in barometric pressure. Estimates of long-term integrated methane emissions from landfills based on such measurements will inevitably yield large uncertainties. The results demonstrate the need for continuous measurements to estimate the annual totals. Preliminary results also show that the stoichiometric model probably works well when the waste is at fully anaerobic condition. The comparison of landfill CH4 oxidation fraction from the model corresponded reasonably well with the estimation from the isotopic method. The difference between two methods likely was due to the different footprint areas. The eddy covariance method is a powerful tool for studying the trace gases and energy fluxes at the surface layer of the atmosphere. It has been widely used to measure CO2, H2O, CH4, and N2O over various ecosystems. The main advantages of the eddy covariance method over other methods are capability of automation for continuous measurements and no disturbance to the surface of the landfill. Without these advantages, we wouldn’t obtained the dataset reported in this paper.

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Chanton, J., and K. Liptay. 2000. Seasonal variation in methane oxidation in a landfill cover soil as determined by an in situ stable isotope technique. Global Biogeochemical Cycles. 14, 5160. Czepiel, P. W., J. H. Shorter, B. Mosher, E. Allwine, J. B. McManus, R. C. Harriss, C. E. Kolb, and B. K. Lamb. 2003. The influence of atmospheric pressure on landfill methane emissions, Waste Management. 23, 593-598. Goldsmith, C. D., J. Chanton, T. Abichou, N. Swan, R. Green, and G. Hater. 2012. Methane emissions from 20 landfills across the United States using vertical radial plume mapping. Journal of the Air & Waste Management Association. 62(2), 183-197, doi:10.1080/10473289.2011.639480. Li, J., R.B. Green, D.A. Magnusson, J. Amen, E.D. Thoma, T.A. Foster-Witting, D.K. McDermitt, L. Xu, G. Burba. 2015. Using eddy covariance to quantify methane emissions from a dynamic heterogeneous area. Extended Abstract for A&WMA’s 108th Annual Conference. June 22-25, 2015. Raleigh, North Carolina. Liptay K., Chanton J. 1998. Use of stable isotopes to determine methane oxidation in landfill cover soils. Journal of Geophysical Research, Atmospheres. 103:D7, 8243-8250. Lohila, A., T. Laurila, J. Tuovinen, M. Aurela, J. Hatakka, T. Thum, M. Pihlatie, J. Rinne, and T. Vesala. 2007. Micrometeorological measurements of methane and carbon dioxide fluxes at a municipal landfill. Environmental Science and Technology. 41, 2717-2722. Mattson, M. D., and G. E. Likens. 1990. Air pressure and methane fluxes. Nature. 347, 718-719. McQuaid, J., and A. Mercer. 1991. Air pressure and methane fluxes. Nature. 351, 528. Poulsen, T. G., M. Christophersen, P. Moldrup, and P. Kjeldsen. 2003. Relating landfill gas emissions to atmospheric pressure using numerical modeling and state-space analysis. Waste Management and Research. 21, 35-366. Shurpali, N. J., S. B. Verma, and R. J. Clement. 1993. Seasonal distribution of methane flux in a Minnesota Peatland measured with eddy correlation. Journal of Geophysical Research. 98, 20,649-20,655. Tokida, T., T. Miyazaki, M. Mizoguchi, O. Nagata, F. Takakai, and A. Kagemoto. 2007. Falling atmospheric pressure as a trigger for methane ebullition from peatland. Global Biogeochemical Cycles. 21:GB2003, doi:10.1029/2006GB002790. Verma, S. B., D. D. Baldocchi, D. E. Anderson, D. R. Matt, and R. J. Clement. 1986. Eddy-fluxes of CO2, water vapor, and sensible heat flux over a deciduous forest. Boundary Layer Meteorology. 36, 71-91. Xu, L., X. Lin, J. Amen, K. Welding, D. McDermitt. 2014. Impact of changes in barometric pressure on landfill methane emission. Global Biogeochemical Cycles. 28, doi:10.1002/2013GB004571. Young, A. 1990. Volumetric changes in landfill gas flux in response to variations in atmospheric pressure. Waste Management and Research. 8, 379-385.

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