Large Methane Emissions From the Pantanal During Rising Water‐Levels Revealed by Regularly Measured Lower Troposphere CH4 Profiles

The Pantanal region of Brazil is the largest seasonally flooded tropical grassland and, according to local chamber measurements, a substantial CH4 source. CH4 emissions from wetlands have recently become of heightened interest because global atmospheric 13CH4 data indicate they may contribute to the resumption of atmospheric CH4 growth since 2007. We have regularly measured vertical atmospheric profiles for 2 years in the center of the Pantanal with the objectives to obtain an estimate of CH4 emissions using an atmospheric approach, and provide information about flux seasonality and its relation to controlling factors. Boundary layer‐free troposphere differences observed in the Pantanal are large compared to other wetlands. Total emissions based on a planetary boundary layer budgeting technique are 2.0–2.8 TgCH4 yr−1 (maximum flux ∼0.4 gCH4 m−2 d−1) while those based on a Bayesian inversion using an atmospheric transport model are ∼3.3 TgCH4 yr−1. Compared to recent estimates for Amazonia (∼41 ± 3 TgCH4 yr−1, maximum flux ∼0.3 gCH4 m−2 d−1) these emissions are not that large. Our Pantanal data suggest a clear flux seasonality with CH4 being released in large amounts just after water levels begin to rise again after minimum levels have been reached. CH4 emissions decline substantially once the maximum water level has been reached. While predictions with prognostic wetland CH4 emission models agree well with the magnitude of the fluxes, they disagree with the phasing. Our approach shows promise for detecting and understanding longer‐term trends in CH4 emissions and the potential for future wetlands CH4 emissions climate feedbacks.

methane is thus a major concern. Unlike CO 2 , CH 4 undergoes chemical reactions in the troposphere, primarily oxidation by OH radicals (Cicerone & Oremland, 1988;Levy, 1971), one of the reasons why CH 4 levels in the troposphere are lower than CO 2 levels. Methane sources can be categorized into natural and anthropogenic sources (e.g., Saunois et al., 2016Saunois et al., , 2020. The main anthropogenic sources include emissions resulting from agriculture and waste (∼35% of total emissions), oil, coal and gas production (∼20%), and biomass burning (∼6%). Production and emission of methane from wetlands is the primary natural source, estimated to account currently for approximately 30% of the total (Saunois et al., 2016(Saunois et al., , 2020. Production of methane in wetlands is the result of anaerobic respiration of organic carbon compounds by methanogens under specific pH and redox conditions (e.g., Baker-Blocker et al., 1977;Bridgham et al., 2013). Partitioning the atmospheric methane budget into emission sectors remains a challenge (e.g., Saunois et al., 2020). Indeed, controls on neither decadal-scale nor interannual variations of atmospheric methane are fully understood. For example, a well-known feature of the atmospheric methane record is a period starting in 1990 when atmospheric methane concentrations seemed to start to level off toward a constant value around 2006, suggesting a stationary state may have been reached (Dlugokencky et al., 1998). However, the growth abruptly resumed in 2007 and rebounded to a similar or faster growth to that of the 1980s. In contrast to previous growth periods, the resumption of the atmospheric CH 4 growth rate in 2007 was associated with atmospheric δ 13 CH 4 , the fraction of atmospheric methane containing carbon-13 instead of carbon-12, which started to decrease. Despite this additional isotopic fingerprint, the cause for resumed growth has not yet been fully attributed to changes in source sectors. Nonetheless, the decreasing trend in δ 13 CH 4 raises the possibility of a wetland emission-climate feedback (e.g., caused by increased precipitation, warming, or increases in biomass production) (Nisbet et al., 2016). Indeed, occurrences of large floods have increased in Bolivia which contains the Llanos de Moxos seasonally flooded wetlands, the contrast between wet and dry season precipitation in Amazonia has increased and substantial parts of tropical South America have experienced particularly rapid surface air temperature warming rates (Barichivich et al., 2018;Gloor et al., 2018;Jiménez-Muñoz et al., 2013;Ovando et al., 2015). Furthermore, unlike for CO 2 , ENSO (El Niño-Southern Oscillation) climate variations do not have a directly visible influence on interannual variation of the atmospheric CH 4 growth rate, another aspect of the global CH 4 cycle which is also not fully understood. Because of the large contribution of total CH 4 emissions from wetlands, changes of these emissions may indeed have possibly contributed to the resumption of atmospheric CH 4 inventory growth. A substantial fraction of global wetlands is located in the tropics (e.g., Keddy et al., 2009). They host several major seasonally flooded savannahs as well as major seasonally flooded floodplains of large rivers like the Amazon, the Paraná, and the Congo Rivers. In South America, major seasonally flooded savannahs include the Llanos de Moxos (Bolivia), the Orinoco savannahs (Venezuela), and the Pantanal (Brazil), of which the Pantanal is the largest (estimates of its area range from 140,000 to 180,000 km 2 , e.g., Diegues, 1994;Hamilton et al., 2002;Junk et al., 2014;Keddy et al., 2009) (Figure 1).
Given this background, and as part of a larger recent effort by a UK-funded consortium (MOYA, "Methane Observations and Yearly Assessments") to obtain improved tropical wetland CH 4 emissions, we report here results obtained from atmospheric concentration measurements over the Pantanal. Our approach takes advantage of the flux-integrating nature of the planetary boundary layer (PBL), which is the result of strong mixing caused by near-surface turbulence, but slow air exchange between the boundary layer and the free troposphere. Surface-to-atmosphere gas fluxes accumulate along air parcel trajectories, initially primarily in the PBL (height above ground on the order of 2 km) (e.g., Chou et al., 2002), causing distinct concentration differences between the PBL and the free troposphere. This signal is representative for fluxes from a large area. The area should scale roughly with the square of the air-mass trajectory path length over a timescale of the exchange time between the PBL and the free troposphere (a length scale of a few hundred kilometers).
The measurements presented here complement earlier CH 4 flux estimates for several subregions of the Pantanal based on flux chamber measurements (Hamilton et al., 1995;Marani & Alvala, 2007) with a largescale integrating atmospheric approach. Besides providing an integral estimate of CH 4 flux from the Pantanal, we aim to characterize the time-variation of fluxes and thus contribute to understanding of some of the controls of CH 4 fluxes. Measurements consist of vertical CH 4 profiles up to 4.4 km height measured roughly every month over a period of approximately 2 years, thus covering nearly two full seasonal cycles. Using these data, we estimate fluxes with a variation of the traditional air-column budgeting technique and a global inverse model of 3-D atmospheric transport. To put the flux data into a longer-term context, and to 10.1029/2021GB006964 3 of 14 help understand the emission seasonality and process, we also use estimates of water levels, burned area and air-column CH 4 estimates obtained based on reflectance data measured on the GOSAT satellite. Finally, we compare our results with predictions with wetland CH 4 emissions models and assess what they may imply for wetland emissions modeling.

Study Region
The Pantanal region is an extraordinarily flat, low-elevation (∼100 m above sea level) plain located centrally in South America, to the south of the Amazon basin ( Figure 1). It is a sedimentary basin in a tectonic depression (Assine et al., 2004). The plain is surrounded by a half-circle-shaped mountain range stretching north-east-south around the basin while it is not bordered by mountains to the west. The headwaters of the Paraguay River are located in the Pantanal. Further downstream, the Paraguay River joins the Paraná River which in turn enters the Atlantic Ocean in Buenos Aires. The Pantanal is seasonally flooded (e.g., Alho et al., 2012). This flood rhythm reflects the strong seasonality of precipitation in the highlands north-east of the Pantanal, the waters of which drain into the Pantanal. Precipitation in the Pantanal itself has also a strong seasonal cycle. Rain starts in September with rainfall on the order of 50 mm mo −1 . It peaks around January to February with approximately 200 mm mo −1 , while there is almost no rain during June to August  (Prigent et al., 2020) which reveal the major South American wetlands. The map also includes the sites where CH 4 profile data have been measured regularly and which are used in this study: TAB (Tabatinga), RBA (Rio Branco), SAN (Santarem), and Pantanal, (b) wetland fraction in the Pantanal during low water (December) and the Paraguay River stage site at Bahia Negra, and (c) during high water levels (June/July).
(e.g., Ivory et al., 2019). Flooding of the region lags peak precipitation by close to half a year with peak flooding occurring typically around July (e.g., Figure 3c). Vegetation of the Pantanal can be characterized as follows (Evans et al., 2014): The wide gently westward sloping fan to the east of the Paraguay River, the main water stem of the Pantanal, is covered by "open wood savannah" (grassland interspersed with trees) (approximately 50% of the Pantanal by area) (Figures 1b and 1c). Then, along the Paraguay River, land cover is swampy mixed savannah and grasslands, and open water (approximately 20% by area) (Figures 1b  and 1c). Woodlands occur primarily in the north-east and, together with riparian forests, cover roughly 14% of Pantanal's area. Finally, agriculturally used land located mainly at the eastern fringes account for 6% by area (Evans et al., 2014).
Water movement in the Pantanal is slow and oxygen levels are often very low. Based on numerous measurements, the low oxygen levels have been attributed to respiration of aquatic vascular plant material (Hamilton et al., 1995). These measurements also revealed seasonally highly supersaturated CH 4 levels in the water column attributed to influx of methane from the sediments produced by methanogenesis (Hamilton et al., 1995).
Population density in the Pantanal is low (Schulz et al., 2019). During the driest part of the year and the beginning of the wet season there is a strong increase in fires. Fires typically start in the middle of the dry season (July) and peak in September. From December onwards fire frequency returns to very low values as seen, for example, by fire counts measured by the Moderate Resolution Imaging Spectroradiometer (MODIS) (Boschetti et al., 2019;Giglio et al., 2018).
One aspect of the Pantanal is that CH 4 emissions are potentially not well represented in current prognostic global wetland CH 4 emission models. This is a consequence of its very flat topography. Existing prognostic models predict flooded area based on terrain slope ("topographic index," TOPMODEL, Beven & Kirkby, 1979) and assume that the hydraulic gradient is proportional to terrain slope (JULES land surface model, Gedney & Cox, 2003; Lund-Potsdam-Jena model-wsl version (LPJ-wsl), Zhang et al., 2016). This last assumption is not correct if topography is quite flat (personal comm. Mike Kirkby).

Regular Vertical Profile Sampling of Lower Troposphere CH 4 , CO, and CO 2 Using Small Aircraft
To determine CH 4 fluxes from the Pantanal region, we have measured vertical CH 4 dry air mole fraction profiles on roughly a monthly basis using small aircraft. The profiles extend from near the ground to approximately 4.4 km altitude. Sampling was performed using an array of flasks, integrated into a suitcase, which were filled sequentially during aircraft descent with valves being opened and closed by a programmable microcontroller. Typically, 17 flasks were filled for each profile with approximately 200 m vertical distance between each sample ( Figure S2). The suitcase with the flasks was then sent to the high precision Greenhouse Gas analysis laboratory (LAGEE) at INPE (Instituto Nacional de Pesquisas Espaciais) at Sao Jose dos Campos, Brazil. At LAGEE dry air mole fractions of CO 2 , CH 4 , and carbon monoxide (CO) of flask air were determined relative to World Meteorological Organization calibration scales. We started the measurements on March 3, 2017 and the last profile was taken on September 30, 2019. The vertical profile samples were all taken during midday over the center of the Pantanal (approximate coordinates 19.45°S, 56.4°W). To reach this point, a small aircraft flew from Campo Grande to the center of the Pantanal (distance approximately 240 km in north-westerly direction). It then descended from 4.4 km altitude above ground to 0.3 km before returning back to Campo Grande. On one return flight, we additionally filled a sequence of air flasks all the way back to Campo Grande permitting a limited assessment of the horizontal extent of CH 4 elevations in the PBL above the Pantanal.

Atmospheric Column CH 4 Estimates Based on Reflectance Data Measured by a Fourier-Transform Spectrometer in the Shortwave Infrared on the GOSAT Satellite
To corroborate results obtained from the vertical profile data, we also use whole air-column CH 4 estimated from space by instruments on the GOSAT satellite (Kuze et al., 2009). Whole-air-column CH 4 is derived from radiance differences of sunlight traversing the atmosphere twice versus light directly received by the sensor on the satellite using the approach of Frankenberg et al. (2005). The method estimates the CH 4 /CO 2 ratio instead of CH 4 alone to minimize systematic errors, which are assumed to affect both CH 4 and CO 2 absorption along the light path and thus largely cancel each other. The method needs an independent estimate of whole column CO 2 to convert the CH 4 /CO 2 ratio to atmospheric column CH 4 . Whole-air-column CO 2 is estimated using transport model simulations of atmospheric CO 2 using realistic CO 2 surface fluxes. A quantitative comparison of retrievals with in situ vertical profile air concentration data at the three Amazonian sites in Figure 1a of Webb et al. (2016) revealed good agreement of the column retrievals and the in situ data. A detailed description of method and data are given in Parker et al. (2011Parker et al. ( , 2020. This study uses Version 7.2 of the University of Leicester GOSAT Proxy XCH 4 .

Flux Estimation Using Atmospheric Air-Column Budget
We exploit PBL versus free troposphere CH 4 differences to obtain flux estimates. Assuming well-mixed conditions in the PBL and that exchange of air between the PBL and free troposphere can be described by an air exchange rate Q (m 3 m −2 h −1 ), the time rate of change of mean PBL dry air mole fraction is given by is dry air molar ratio,  PBL E and  free trop E are dry air mole fraction in the PBL and in the free troposphere, respectively, t time (h), h PBL height (m), n air molar density (mol m −3 ), F srf flux to the atmosphere (mol m −2 h −1 ), z vertical coordinate (m), u wind velocity (m h −1 ), andindicates a PBL average (Chou et al., 2002 (a detailed derivation is provided in the Supporting Information S1). The first term in parentheses on the right of Equation 1 tends to be small compared to the other two terms. Thus, given an estimate of PBL-free troposphere air exchange time  E , PBL-average wind speed and PBL-free troposphere difference and its largescale gradient, then the surface flux can be estimated. We estimate here the large-scale gradient  the GOSAT retrievals (PBL-free troposphere differences decline to 0 over a spatial scale of ∼700 km downwind, Figure S4). For our approach to hold, it is also necessary that the PBL-free troposphere differences are caused by fluxes from the region in question and not advected from remote regions where there are large CH 4 fluxes, such as the Amazon.

Flux Estimation Using Inverse Modeling of 3-D Atmospheric Transport
We also use the variational inverse model INVICAT  based on TOMCAT, a global 3-D Eulerian atmospheric transport and chemistry model (Chipperfield, 2006;Monks et al., 2018) for flux estimation. Fluxes are estimated by minimizing the sum of the mismatch between uncertainty-weighted observed and simulated atmospheric trace gas mixing ratios, here CH 4 , and simultaneously between prior and posterior CH 4 fluxes. The data assimilated include CH 4 retrievals based on radiances measured by instruments on GOSAT as described above , in situ measured CH 4 mole fractions at the surface station network operated by NOAA Global Monitoring Laboratory and the CH 4 mole fraction data measured at the center of the Pantanal. The set of prior guess flux emissions are described in detail in Wilson et al. (2021) as well as in the Supporting Information S1. The spatial resolution of the model is 5.6° × 5.6° which is quite coarse but sufficient for this study.

Inundated Area
We use the GIEMS (Global Inundation Extent from Multisatellites) estimates of inundated area of Prigent et al. (2020). Existing estimates, which cover the period from January 1992 to December 2015, have been complemented for the Pantanal region by the data for the years 2016-2018 for this study. For technical reasons similar estimates for 2019 cannot yet be obtained. Fraction of inundated area is estimated monthly with 0.25° × 0.25° spatial resolution. Identification of wetland area is based on passive microwave radiation (difference between vertically and horizontally polarized radiation), active microwave backscattering (backscattering coefficient) and near-infrared reflectance (via NDVI, normalized difference vegetation index) (Prigent et al., 2020).

River Stage Height
As an indicator of flood levels during 2019 and 2020, when GIEMS inundated area estimates are not available, we use here river stage records measured at Bahia Negra ( Figure 1) by ANA (Agencia Nacional de Aguas e Saneamento Basico, Brazilian Hydrological Service).

Burned Area
As a proxy for CH 4 emitted by biomass burning, we use burned area estimates based on data measured by MODIS on the Terra and Aqua satellites (Boschetti et al., 2019;Giglio et al., 2018). Briefly, the algorithm uses vegetation index changes over time to identify burned areas and corroborate fires as the cause with fire spots measured by remote sensing from temperature anomalies. The accuracy of the burned area estimator has been assessed in various ways, including comparisons with manually interpreted Landsat images (Giglio et al., 2018). While the estimator misses approximately 25% of fires, this is unlikely to affect assessment of interannual variation for which it is used in this study (Giglio et al., 2018).

Global Wetland Model CH 4 Flux Predictions
Our results are potentially of interest for prognostic wetland CH 4 emissions models used to analyze global atmospheric CH 4 patterns in space and time and also as components of Earth system models. Here we use predictions of the LPJ-wsl dynamic global vegetation model, developed for carbon cycle applications based on the original LPJ global vegetation model (Sitch et al., 2003). LPJ-wsl models surface inundation using the overland flow hydrological TOPMODEL (Beven & Kirkby, 1979;Zhang et al., 2016), which is used in a prognostic wetland CH 4 emission model (Zhang et al., 2018).

Results
To help interpret the atmospheric CH 4 concentration data, we use two indicators of water levels: inundated area extent estimated with remote sensing (GIEMS) and measurements of Paraguay River stage levels. The records agree fairly well with regards to seasonality (phasing) and to some extent with regards to interannual variation (Figure 2). We therefore use the stage level record as an indicator of the temporal course of flood levels in 2019/2020 when inundated area extent data from remote sensing are missing. The records indicate that flood levels during the period of CH 4 measurements were average in 2017 and high in 2018. After 2018, flood levels decreased again and reached very low levels in 2020 ( Figure 2b). Furthermore, both records show that peak flooding occurs during the middle of the year, while the lowest flood levels occur around the turn of the year (December and January). This time pattern is confirmed by a wetlands index (NDWI normalized difference water index), measured by MODIS (not shown).
Both seasonal and interannual variation in flood levels are roughly tracked by area burned. Generally burned area tends to be large following a year with comparably low maximum water level. There are more years with high burned area pre-2011 compared to 2012 to 2019. Water levels returned to low values in 7 of 14 2020 when fire frequency and extent have increased to very high levels (not visible in Figure 2c because the record ends in December 2019). In 2020 around 30% of the entire Pantanal area burned (e.g., Mega, 2020). Fires in the Pantanal are predominantly human-caused (e.g., Vigano et al., 2018).
As mentioned above, the difference of PBL mean CH 4 and free troposphere CH 4 indicates the existence and to some extent magnitude of surface-atmosphere fluxes. Vertical profiles do indeed show pronounced elevations in the PBL compared to the free troposphere ( Figure 3). The PBL-free troposphere differences reveal a strong seasonality, with flux from the Pantanal to the atmosphere starting just after flood levels have reached their lowest levels. According to PBL-free troposphere differences fluxes increase rapidly during the rise of the water levels, decrease toward the end of the rise and remain low after maximum water levels have been reached (e.g., during peak flood in mid-2018 onwards and similarly from July 2019 onwards). The CH 4 fluxes are not caused by fires as the high CO levels precede high CH 4 values (Figure 3c). The high CO levels are the result of biomass burning and thus indicate the onset and end of the burning season. This is confirmed  fluxes estimated based on the atmospheric CH 4 vertical profiles suggests that a large flux of CH 4 is emitted during the early ascending phase of water levels during the end of 2017 and early 2018.
As mentioned above, we estimate CH 4 fluxes in two ways. Our first approach based on PBL-free troposphere differences is applicable if these differences are caused by fluxes from the region in question. Back-trajectories calculated for each measurement of a profile during the first year of measurements indicate that air masses have indeed not crossed other major CH 4 emission regions, like Amazonia or Llanos de Moxos, and that air masses travel mostly in the lower troposphere in the surroundings of the Pantanal ( Figure S3). To integrate fluxes spatially we assume that they occur spatially homogeneously over Pantanal's flooded area. We thus multiply our flux estimates (interpolated to monthly values) with monthly flooded area estimates of Prigent et al. (2020). We do this for the overlap period of flooded area estimates and CH 4 flux estimates derived from vertical CH 4 profiles (2017)(2018). We obtain emissions estimates ranging between 2.0 and 2.8 TgCH 4 yr −1 for mean PBL wind speeds ranging between 10 and 15 m s −1 , respectively (estimated from air-mass trajectories) with fluxes varying between 0 and 0.4 gCH 4 m −2 d −1 . In contrast, the flux estimate estimated by the 3-D atmospheric transport inversion for the entire Pantanal grid cell is  3.5 3.5 E TgCH 4 yr −1 ( Figure S1 and Table S1).

Discussion
In the following, we first compare the observed Pantanal PBL-free troposphere differences with equivalent values measured above other large-scale wetlands as an indicator of Pantanal flux strength compared to other regions. We then discuss the flux time series relative to water levels revealed by our data and what may determine the observed time course. In order to confirm what our vertical profile data reveal about flux time course we compare them with whole air-column retrievals based on remote sensing which also permits an assessment of the flux strength versus flooded area relationship. Finally, we compare interannual variation and seasonality of fluxes based on our analysis with a widely used global prognostic wetland CH 4 emissions model.
Our vertical profile data reveal episodically large PBL-free troposphere CH 4 differences of up to 300 ppb. For wetlands these are comparably very large enhancements. For comparison, enhancements at two sites in the western/central Amazonia, Rio Branco and Tabatinga, Brazil (Figure 1a), where regular vertical profiles have been measured by LAGEE on a regular basis since 2010, reach enhancement levels up to ∼120 ppb ( Figure S5). PBL-free troposphere CH 4 differences at Santarem, where profiles have been measured since 2000 (Basso et al., 2016;Miller et al., 2007) (Figure S5), are larger, up to 160 ppb, but nonetheless still substantially smaller compared to Pantanal. Rio Branco and Tabatinga data are expected to sample a somewhat diffuse signal of CH 4 emissions from large seasonally flooded areas to the east of the sites (e.g., Figure 1 in Gatti et al., 2014) while the nature of the source causing the comparably large PBL-free troposphere differences at the Santarem site are not fully understood. These three records reveal also a seasonal cycle suggesting a role played by the Amazon flood pulse. According to Pangala et al. (2017) at these sites emissions via tree stems living in floodplains, functioning as ducts during the seasonal flood, and emissions from open surfaces contribute approximately equally to the total flux. One region where similarly large but temporally less coherent PBL-free troposphere differences compared to the Pantanal have been measured are the West Siberian lowland wetlands (Sasakawa et al., 2017), a vast waterlogged area located between the Ural Mountains (approximately 60°E) and the Jenissey River (approximately 90°E).
A second interesting feature suggested by the Pantanal measurements is that methane seems to be released in large amounts once the minimum flood levels have passed and levels are increasing again. Emissions start to decrease before maximum flood levels have been reached. To confirm these CH 4 release dynamics, as well as to confirm that the measured CH 4 elevations are caused by Pantanal emissions (i.e., differ distinctly from background air), we compared remote sensing-based retrievals from GOSAT for the Pantanal with two reference regions: Brasilia (Mato Grosso), located to the north-east of the Pantanal, and Gran Chaco, located to the south-west (Figure 4). These comparisons do also suggest a quite sudden onset of CH 4 emissions with this occurring just after flood levels have reached their minimum and that maximum emissions precede maximum inundated area (see also Figure S6 which further supports these dynamics). Particularly sharp increases occur in 2011, 2015, and 2017. As an aside, since the enhancements and their variation in time are similar when we use a reference located north-east from the Pantanal and a reference located south-east, the air-column CH 4 enhancements (compared to the reference) must indeed be caused by emissions from the Pantanal and not advected from far remote regions in South America like, for example, the Amazon (see also Figure S3).
The reason for the large, quite sudden CH 4 release during low water levels and decrease of flux before reaching maximum flood level is not clear. The CH 4 build-up may be related to transport of fresh decomposable organic matter via the waters from the highlands feeding the Pantanal, which provide substrate for methanogenic bacteria and may also determine the time course of respiration of organic matter and thus oxygen levels in water (Hamilton et al., 1995). Hamilton et al. (1997) indeed demonstrate that oxygen levels in the Paraguay River decrease to very low values during the rising stages of the water, while oxygen levels rapidly rise during the fall of stage levels (their Figure 5). This suggests that depletion of the organic matter pool provided by transport from the "catchment" (or in the rivers themselves) of the river by respiration and methanogenesis takes two to three months. The timing of methane release may also be related, in part, to comparably short gas bubble pathways through the water column and comparably low hydrostatic pressure during initial phase of water-level rise. Direct measurements (Enns et al., 1964) show that saturation pressure of dissolved gases in water increases with pressure, e.g., in the oceans with depth, as a result of increasing hydrostatic pressure, in agreement with predictions of thermodynamics. Several studies observed differences in CH 4 ebullition rates depending on water depth above sediments where methane was formed and atmospheric pressure (e.g., Keller & Stallard, 1994;Mattson & Likens, 1990). The explanation for this phenomenon may be that saturation partial pressure increases with total pressure (sum of atmospheric pressure and hydrostatic pressure of the water column) and that the process of forming a gas bubble involves work against external pressure and surface tension ( Figure 5).
Our vertical CH 4 profile sampling occurred during a medium to wet period with high water levels in 2018 ( Figure 2). Whole-air-column CH 4 retrievals using remote sensing which cover a longer time period can give some indication how CH 4 emissions vary during wetter versus drier years ( Figure 4). These data suggest that CH 4 emissions are larger during wetter years. For example, in 2012, a year with low water levels, air-column CH 4 signals are substantially smaller compared to the high water-level year in 2018.
How do our results compare with independent estimates for the Pantanal, other natural CH 4 sources in South America and more generally other wetlands? The total CH 4 emissions estimated based on our approach exploiting PBL-free troposphere differences are somewhat smaller than 3.3 TgCH 4 ( E 30% uncertainty estimated from data in their figures) net annual CH 4 emissions from the Pantanal estimated by Marani and Alvala (2007) using flux chambers and an annual mean flooded area estimated based on river stage levels. They are also smaller than an estimate of Melack et al. (2004) (also 3.3 TgCH 4 yr −1 ), who multiplied CH 4 flux estimates from Amazonia with flooded area estimates. The uncertainty of this latter estimate is likely of similar order as the Marani and Alvala estimate.
We may also compare these values with estimates of CH 4 emissions from Amazonia. Recent converging estimates both from global atmospheric transport inverse modeling approaches, similar to the one described here, and a large set of surface flux measurements scaled up to the Amazon basin are ∼35-50 TgCH 4 yr −1 (Pangala et al., 2017;Ringeval, 2014;   Tunnicliffe et al., 2020;Wilson et al., 2016Wilson et al., , 2020, approximately 25-30% of global wetland emissions of ∼180 TgCH 4 yr −1 (Saunois et al., 2016(Saunois et al., , 2020. Depending on the method used, the CH 4 emissions from the Pantanal are thus on the order of 4-8% of Amazon River catchment CH 4 emissions. Based on synthetic aperture radar data measured from space (Hess et al., 2015), the Amazonian wetlands area is estimated to be ∼8.4 × 10 5 km 2 with flooded fraction of this area varying between 34% and 75%. In percentage terms, the Pantanal maximum inundated area to Amazonia maximum inundated area ratio is thus on the order of 10%.
It is of interest to compare our results with wetland CH 4 emission model predictions as this may possibly suggest further improvements. Comparison with the LPJ-wsl model 2018 version predictions and JULES (not shown) reveal the following. Both models predict a seasonality with flux magnitude of peak fluxes similar to our estimates. The total annual flux predicted by the LPJ-wsl model for September 2017 to August 2018 is 2.2 TgCH 4 yr −1 (region used to estimate total flux: 24°S to 18°S, and 60°W to 55°W, respectively). This estimate is at the lower end of the results based on the atmospheric approaches. The seasonality of fluxes of LPJ-wsl is highly correlated with water levels with no lags between the two. Thus, this model does not reproduce the observed several months phase shift between maximum fluxes and maximum water levels. Comparison of the LPJ-wsl model predictions of flooded area with Figure 2a furthermore shows that interannual variability of flood levels is captured to some extent (as mentioned earlier and also confirmed by NDWI estimates of flooded area based on data measured by MODIS on satellites). This is likely the result of overland flow not being yet well represented in these models (for the reasons explained above).
Finally, we discuss the pros and cons of our vertical profile troposphere greenhouse gas sampling approach. A main value is that it reveals clearly the seasonality of fluxes. If extended over several years, it will add to our understanding of the cause of interannual variation and thus refine our understanding of controls, and potential future feedbacks. This aspect of our approach distinguishes it from one-off campaigns. It adds to on-the-ground direct flux measurements of Marani and Alvala (2007) for the Pantanal, or Pangala et al. (2017), Melack et al. (2004), and Barbosa et al. (2020) for Amazonia in that the seasonality of the fluxes come out clearly. Our approach focusing on PBL-free troposphere differences is suited for well-localized flux regions. It could be made more precise by measuring PBL-free troposphere exchange time rate e.g., using additional tracers such as O 3 or 222 Rn although at some cost (see e.g., Chou et al., 2002). The vertical greenhouse gas profile data can of course also be used in atmospheric transport inversions of Eulerian models (as in this study), as well as Lagrangian models (e.g., Lin et al., 2003;Miller et al., 2007).

Summary
We have reported on CH 4 emission estimates from the Pantanal, the largest tropical seasonally flooded savannah. The estimates are based on approximately monthly measured vertical profiles of dry air molar fraction CH 4 vertical profile measurements in the center of the Pantanal from near the ground to approximately 4.5 km height asl, large-scale gradients and inundated area estimated using remote sensing. The data cover the period from March 2017 to September 2019. According to inundated area estimates from remote sensing (Prigent et al., 2020) and river stage records, 2017 was an average year while 2018 was a comparatively wet year. This is also confirmed by burned area records. Flux estimates based on a PBL budgeting technique suggest an annual flux on the order of 2.0-2.8 TgCH 4 yr −1 for 2017 and 2018 while an atmospheric inverse modeling approach using the CH 4 profile data suggest annual emissions on the order of 3.5 TgCH 4 yr −1 . This latter estimate is similar to estimates obtained using flux chambers (Marani & Alvala, 2007). Our data indicate an interesting seasonality of CH 4 emissions which start to rise after water levels have reached their lowest level and halt once maximum water levels have been reached. This dynamic is not reproduced by prognostic wetland CH 4 models we used in this study. These models also do not reproduce interannual variation all that well. Our approach-long-term measurement of lower troposphere greenhouse gas vertical profiles-is attractive for revealing seasonal and longer-term trends which may reveal more clearly sensitivity of wetland CH 4 emissions to changes in climate.

Data Availability Statement
CH 4 profile data can be obtained from the NERC (Natural Environmental Research Council) data archive Centre for Environmental Data Analysis (CEDA) via the link https://catalogue.ceda.ac.uk/uuid/d309a5ab60b-04b6c82eca6d006350ae6.The latest version of the University of Leicester GOSAT Proxy v9.0 XCH4 data are available from the CEDA data repository at https://doi.org/10.5285/18ef8247f52a4cb6a14013f8235cc1eb . The version 7.2 used in this study is available from the Copernicus C3S Climate Data Store at https://cds.climate.copernicus.eu.