The study area is in the Condamine natural resource management region of southeast Surat Basin, Queensland (Fig. 1a). It includes the southeast portion of the Surat Basin CSG field, which is the largest CSG-producing field in Australia with more than 60 % of Australia's total proven gas reserves (Australian Competition and Consumer Commission, 2020). The CSG is primarily produced from coals with high permeability in the middle Walloon Coal Measures (Baublys et al., 2015; Draper and Boreham, 2006; Scott et al., 2007). In the CSG field there are numerous CH4 emission sources including CSG wells (exploration, appraisal, production, and abandoned), field compression stations, central processing plants, gas and water transmission pipelines, and raw water ponds (CSG co-produced water storage) (Fig. 1b). CH4 emitted from agricultural activities is another major source of atmospheric emissions. Grazing cattle herds, feedlots, and dairies are spread throughout the study area, and grazing cattle and feedlots are often adjacent to CSG infrastructure (Fig. 1b). There is also stored animal waste associated with the cattle feedlots and piggeries. Known but poorly quantified sources of CH4 in the study area include bush fires, wetlands, termites, on-farm biosolid fertilisers, emissions from un-capped coal and gas exploration wells, and emissions from an abandoned coal gasification development (Lu et al., 2021).

To support the airborne mass balance estimate of CH4 emissions presented in Neininger et al. (2021), the University of New South Wales (UNSW) prepared a BU inventory for 2018, and comprehensive details of this inventory are provided in Neininger et al. (2021). The UNSW BU inventory is larger than the region within which the IFAA samples were collected (Fig. 1) to allow comparison between the IFAA sample and the upwind BU inventory. The IFAA samples are referenced using a four-number string: the first two numbers are the day in September 2018, and the second two numbers are the sample reference for the day. A full listing of the IFAA samples and their sample location details is presented in Table A2.

The UNSW BU inventory closely followed the methods outlined in Australia's 2018 National Greenhouse Gas Inventory (Australian Government, 2020a). The UNSW inventory covers known sources such as those from the CSG industry and agriculture as well as sources discovered during the 2018 ground campaign in the study area (Lu et al., 2021). The inventory was collated using publicly available data. These data were supplemented with information from environmental impact approval reports, government and industry documents, close inspection of the satellite imagery in Google Earth, and airborne and ground survey observations (discussed in Lu et al., 2021, and Neininger et al., 2021). The locations of the sources contained in the UNSW inventory are shown in Fig. 1b.

In Fig. 2a all point sources (CSG facilities, feedlots, coal mines, etc.) are presented as an emission intensity map, and in Fig. 2b the distributed sources are shown. Distributed sources are multiple small sources spread evenly over a subregion. For example, we know the total number of cattle within a statistical district (Condamine, Burnett Mary, and Queensland Murray–Darling Basin) but not their locations, so the emissions are spread evenly using the population density. Comprehensive details about how the emissions from distributed sources were determined are discussed in Neininger et al. (2021, their Supplement, Sect. S). CSG sources are concentrated in a northwest to southeast zone, with agricultural sources on either side. The UNSW inventory estimate for the CH4 emissions in the southeast portion of the Surat Basin CSG fields for 2018 is 20 900 kg h-1 (183 Gg yr-1). In the UNSW inventory most of the emissions come from cattle, which contribute 50.3 % (29.9 % from grazing cattle, 19.1 % from feedlots, and 1.3 % from dairy cattle); all CSG sources contribute 30.5 %, piggeries 8.7 %, coal mines 7.6 %, and all other sources only 2.9 %. Within the airborne measurement TD domain, the UNSW inventory estimate for CH4 emissions is 11 500 kg h-1 (101 Gg yr-1), and the percentage contribution order within the TD domain is different: CSG 53.7 %, feedlots 19.0 %, grazing cattle 14.1 %, piggeries 7.3 %, coal 3.5 %, and all other sources 2.4 %. The heterogeneity of the point source emission rate is visually apparent in Fig. 2a. Within the UNSW inventory domain, 50 % of point sources have an emission rate of less than 4.5 kg h-1. These point sources account for 59 % of the UNSW inventory total. The top 10 % have an emission rate exceeding 113 kg h-1. The 42 sources in the top 10 % account for 37.7 % of the UNSW inventory total. The largest individual source is an open-pit coal mine (27.28∘ S, 151.71∘ E; red square, Fig. 2a), which emits 843 kg h-1 (4.1 % of the UNSW inventory total). The second largest source is a feedlot (27.42∘ S, 151.14∘ E; orange square, Fig. 2a), which emits 563 kg h-1 (2.7 % of the UNSW inventory total). The largest CSG source is a raw water pond (26.96∘ S, 150.49∘ E; light green square, Fig. 2a), which emits 221 kg h-1 (1.1 % of the UNSW inventory total).

The distributed sources of CH4 are dominated by grazing cattle (dark red in Fig. 2b, 6.54 kg h-1 per 25 km2), followed by the irrigation farming district (light blue, 0.64 kg h-1 per 25 km2), and then the forested areas with kangaroos (purple, 0.09 kg h-1 per 25 km2). There may also be some termite emissions from the forest and agricultural areas, but these have not been quantified. Grazing cattle account for 29.9 % of the UNSW inventory total CH4 emissions, and the position of this large source of CH4 emissions is one of the largest uncertainties in the calculations below. To maintain soil health and grass cover, the grazing cattle are rotated through various fields, and at times the cattle also graze along the roadside. The forested areas with large kangaroo populations were estimated to contribute only 0.2 % of all CH4 emissions. The irrigated agricultural district was estimated to have diffuse CH4 emission sources contributing only 0.7 % towards the UNSW inventory total.

Using airborne measurement techniques, Neininger et al. (2021) quantified the CH4 emissions in the southeastern portion of the Surat Basin CSG fields and surrounding agricultural districts. In the September 2018 campaign, there were 10 flights (∼45 h) using a research motor glider operated by Airborne Research Australia (ARA). Neininger et al. (2021) showed that there was strong correlation between the TD CH4 flux estimate and the UNSW inventory. Within the airborne survey domain, the TD estimate was 13 500 kg h-1 (118 Gg yr-1), which is 1940 kg h-1 (17 Gg yr-1) higher than the UNSW inventory.

The δ13CCH4(s) signatures of 16 primary sources in the Surat Basin were characterised in Lu et al. (2021) using air samples collected during ground-based surveys. These values are listed in Table A1 and were assigned to the different source categories in the inventory to create isotopic source signature maps. The spatial locations of the CH4 point sources and their corresponding δ13CCH4(s) values are shown in Fig. 2a and c. The distribution of the CH4 diffuse sources and corresponding δ13CCH4(s) values are shown in Fig. 2b and d. For many source types only one δ13CCH4(s) signature was determined in Lu et al. (2021). Gaining access to a wide range of farms and CSG facilities is difficult due to operational procedures and health and safety concerns. Therefore, an aim of this study was to examine if IFAA samples can be used to extend our knowledge of the CH4(s) signatures from various sources in the Surat Basin.

From the ground-based studies, the δ13CCH4(s) signatures from CSG processing and production facilities and CSG raw water ponds ranged from -56.7 ‰ to -45.6 ‰ (Bayesian 95 % credible interval (Crl); Lu et al., 2021). CSG is extracted from a range of depths in the Surat Basin gas fields. The shallowest coal measures tend to have a lighter isotopic signature and the deeper coal measures a heavier signature. This is due to the displacement of the original CH4 in coal seams nearest the ground surface with biologically derived CH4 (Iverach et al., 2015, 2017). The reported range for δ13CCH4(s) from gas from the Walloon Coal Measures is -64.1 ‰ to -44.5 ‰ (Baublys et al., 2015; Draper and Boreham, 2006; Hamilton et al., 2014, 2015; Iverach et al., 2015, 2017). The difference between the ground-based studies and well observations highlights the need to better characterise δ13CCH4(s) population statistics of CSG and other CH4 sources.

In addition to CSG sources of CH4 there are four major sources of CH4: feedlots, grazing cattle, piggeries, and coal mines (Neininger et al., 2021). For each of these sources only a single plume has been sampled to estimate δ13CCH4(s); thus many more data sets need to be collected to robustly define the population statistics. A useful measure for the likely range of δ13CCH4(s) for each source category is summarised by the δ13CCH4(s) Bayesian CrIs, which for the limited sampling to date are as follows: feedlots, -65.2 ‰ to -60.3 ‰; grazing cattle, -61.7 ‰ to -57.5 ‰; piggeries -48.0 ‰ to -47.1 ‰; and coal mines, -61.1 ‰ to -58.9 ‰. Refer to Lu et al. (2021) for comprehensive details about how these δ13CCH4(s) signatures were determined and details about Bayesian regression.

For CH4 source categories listed in the BU inventories that were not sampled during the mobile survey, δ13CCH4(s) signatures were obtained from the literature. These include the δ13CCH4(s) signatures for kangaroos (-80 ‰, Godwin et al., 2014), on-farm waterbodies (dams) (-51.2 ‰, Day et al., 2016), and domestic wood heaters and native vegetation wildfires (-22.2 ‰, Ginty, 2016). There are also numerous termite mounds in the region, but there have been no studies on the rate of CH4 emissions from these mounds nor has δ13CCH4(s) been characterised for termites in the region. For worker termites collected from mounds near Darwin, Australia, Sugimoto et al. (1998) reported δ13CCH4(s) values ranging from -88.2 ‰ to -77.6 ‰. A major gas distribution line passes through the region; this transports conventional gas from the fields to the west of the study area to the LNG terminals on the coast and for the domestic market at Brisbane (Jemena, 2021). The δ13CCH4(s) population statistics for this gas are not known.

Collecting IFAA samples in FlexFoil or similar bags is a comparatively fast and cost-effective method and has been used in numerous airborne and ground-based CH4 studies (Fisher et al., 2017; France et al., 2021; Lowry et al., 2020; Menoud et al., 2022b). During the campaign in September 2018, 92 IFAA samples were collected on board a Diamond Aircraft HK36TTC ECO-Dimona, equipped with underwing pods that housed the Los Gatos Research ultraportable greenhouse gas analyser and the modified LI-COR LI-7500 open path gas analyser for fast CO2 and H2O measurements and meteorological sensors for wind and thermodynamic parameters. Specifications of the airborne platform and instruments are described in Neininger et al. (2021). Sample bags were manually filled in the cockpit by connecting them to an air sampling tube, which had an inlet mounted far outside of the fuselage under the wing. Air was drawn into 3 L SKC FlexFoil PLUS (SKC Inc., USA) sample bags with polypropylene fittings. Ambient air was drawn from the intake with the assistance of a Viton membrane pump via polyurethane tubing. Before opening the valve of the sampling bags, the fitting was carefully flushed to avoid sampling cockpit air. The duration of bag filling was ∼ 1 min, which covers a track length of about 3 km at the flying speed of ∼ 170 km h-1. All IFAA samples presented in this study were collected within the convective boundary layer. During each flight, the top of the convective boundary layer was established several times by ascending and descending between the lower transects. During the surveying period, the convective boundary layer typically had an upper altitude limit ranging from 1700 to 2700 m a.g.l. (Neininger et al., 2021). Most of the airborne measurement surveying for the mass balance surveying and IFAA sampling was flown at altitudes of approximately 150 and 300 m a.g.l. (Fig. 3a). IFAA samples were collected on each transect, with up to 25 samples being collected in 1 d. When CH4 plumes were identified from the on-board real-time display, additional samples were collected. The IFAA sample locations for the 4 d analysed below are shown in Fig. 1a.

When collecting IFAA samples there are many sampling and logistical challenges. We collected 3 L samples of air to enable both on-site testing and accurate laboratory measurements, and we used SKC FlexFoil PLUS bags to reduce the cost of the project. Also, because the air samples were collected manually and stored in the cockpit, the number of samples collected in each sampling run was limited to a maximum of ∼ 15. A purpose-built sampling system that rapidly fills 1 L canisters would potentially enable in-plume higher mole fraction IFAA samples to be collected. The smaller canisters would also allow for more samples to be collected on each flight. More in-plume samples with higher CH4 mole fraction values would reduce the uncertainty in the derived δ13CCH4(s) signatures. However, if the plume is heterogenous there is also a risk that rapidly filling the canisters will not sample the highest mole fraction portions of the plume.

For each IFAA sample the back-trajectory footprint (BTF) was calculated using the NOAA Air Resources Laboratory's (ARL) HYSPLIT model (Draxler et al., 1998) (Fig. A1 in Appendix A). HYSPLIT was used for this study because it is publicly available, enabling the methods presented here to be replicated by others. The HYSPLIT model is widely used for tracking air parcel trajectories as well as calculating transport, dispersion, and deposition of pollutants and hazardous materials (Stein et al., 2015). In this study, we determine the contributing CH4 sources (from the UNSW BU inventory in Neininger et al., 2021) of an IFAA sample within a BTF based on the 2 h HYSPLIT back trajectory starting at the IFAA sampling height and at the mid-point of the IFAA sampling interval. The HYSPLIT back-trajectory calculations were done using the global data assimilation system (GDAS) 0.5∘ meteorology option (GDAS 0.5∘, global September 2007–June 2019, using the normal trajectory, and for the vertical motion we selected to model the vertical velocity). The 2 h period was based on the forward and inverse plume modelling in Neininger et al. (2021), which established that most of the CH4 enhancement along a flight line could be attributed to a CH4 source located within 2 h, and within 0.025, 0.05, and 0.1∘ longitude/latitude on each side of the IFAA sample collection mid-point 1 and 2 h back-trajectory locations (refer to Fig. A1 for the HYSPLIT back trajectories and Fig. A2 for a representative BTF inventory polygon; also refer to Neininger et al. (2021), Supplement, Fig. SF26, for an example of the more detailed back-trajectory modelling, used to guide the HYSPLIT settings). Using the HYSPLIT BTF to determine contributing sources is an easy-to-replicate method. A more rigorous method would involve forward modelling the mixing of plumes for the prevailing meteorological conditions. Given that there are over 6000 point and distributed CH4 sources in the region, it is beyond the scope of this project to model the plume extending from each source and δ13CCH4(s) mixing. For the goal of identifying major upwind sources of CH4, the HYSPLIT BTF results compared favourably when checked against the higher-resolution local-scale modelling in Neininger et al. (2021). As the wind speeds changed throughout the sampling campaign this results in a different BTF for each sample. However, as will be shown below, for the purpose of identifying inventory knowledge gaps and mitigation opportunities, the variations in the BTF land surface area analysed are not critical for this study.

All CH4 mole fractions and δ13CCH4 values reported below were measured in the greenhouse gas laboratory at Royal Holloway, University of London (RHUL) (Fisher et al., 2006). For quality control, the IFAA samples were analysed on-site prior to shipping to the UK using a Picarro G2201-i cavity ring-down spectrometer (CRDS) (Picarro, Inc., USA). This was done to check for contamination during transportation to RHUL. If the UNSW and RHUL CH4 mole fraction values had a relative difference of greater than 1 %, the samples were removed and not analysed further. Forty-nine useable IFAA samples were collected. These samples had a median CH4 mole fraction difference of 0.4 % between the UNSW and RHUL measurements. The Picarro G2201-i used for this quality control step had been previously calibrated via an interlaboratory comparison between the Commonwealth Scientific and Industrial Research Organisation (CSIRO), UNSW, and RHUL. This calibration used Southern Ocean air from 2014 and 2016. Comprehensive details of the Picarro G2201-i performance are discussed in Lu et al. (2021). To control for any potential instrument drift, standardised Southern Ocean air was analysed at regular intervals, typically every 120 min, and if required, a drift correction was applied.

At RHUL, a Picarro G1301 CRDS (Picarro, Inc., USA) and a modified gas chromatography isotope ratio mass spectrometry (GC-IRMS) system (trace gas and isoprime mass spectrometer, Elementar UK Ltd., UK) (Fisher et al., 2006) were used for the measurement of CH4 mole fraction and δ13CCH4, respectively. The Picarro G1301 CRDS has a reproducibility of ±0.0003 ppm. Air standards from the National Oceanic and Atmospheric Administration (NOAA) were used to calibrate the CRDS to the WMO X2004A scale (Dlugokencky et al., 2005; WMO, 2020). The CH4(a) mole fraction of each IFAA sample was determined by analysing the sample for 210 s on the Picarro G1301, and the average value of the last 90 s was recorded. All IFAA samples were measured in triplicate to obtain δ13CCH4(a) on the Vienna Pee Dee Belemnite (VPDB) scale using GC-IRMS. When the standard deviation of the first three analyses was greater than the target instrument precision of 0.05 ‰, a fourth analysis was performed. For more detailed information about the instrumentation and measurement procedure, see Fisher et al. (2006) and Lu et al. (2021).

Different CH4 formation processes result in each CH4 source having different δ13CCH4 population statistics for both the range and distribution shape (Whiticar, 1999; Sherwood et al., 2017, 2020; Menoud et al., 2022a). Thus, the isotopic composition of air samples can be used to identify inputs from similar sources, the extent of mixing of two or more sources, and samples that are offset to the isotopic composition expected from the BU inventory. IFAA samples of interest are those that have relatively high CH4(a) or different than expected δ13CCH4(a) (below called points of interest) because these samples may indicate over- or underestimation of CH4 emissions in the BU inventory. The points of interest can also indicate that a source of CH4 has been missed in the BU inventory. A point of interest may also indicate sampling or measurement errors, but this is unlikely for the samples analysed, due to the quality assurance measures at all stages of sampling and measurement.

Subsets of samples were collated based on altitude (Fig. 3a) and the dominant CH4 source in the BTF BU inventory (Tables A2, A3 and A4). Before sorting the data into subsets, points of interest were identified by visual inspection using two graphs: the BTF BU inventory vs. IFAA sample CH4 (Fig. 3b) and a Keeling plot (δ13CCH4(a) vs. 1/CH4(a)) (Fig. 3c). Although the points of interest were removed for the Keeling-model regression analysis, they are still analysed in the context of their position within the Keeling plot (Fig. 3c). After the points of interest were identified, the IFAA samples that had a single source that represented over 50 % of the 2 h back-trajectory inventory were combined into sets for the multi-Keeling-model regression with shared parameters analysis. Keeling analysis sets for the following categories were collated:

CSG > 50 % BTF BU inventory, 100–200 m a.g.l.

For coal mines and piggeries there are only two BTF BU inventories with > 50 % emissions from these sources (Tables A3 and A4). As a result, these categories could not be analysed using the modelling methods below. There is only one category for feedlots because there are too few points for the Keeling analysis in the 100–200 and 250–350 m a.g.l. data sets.

For two-endmember mixing (a source of CH4 mixed in background air), the δ13CCH4(s) signature of the source mixing in background air is calculated using the Keeling-model method (Keeling, 1961; Pataki et al., 2003). The Keeling model is 1δ13CCH4(a)=CH4(b)(δ13CCH4(b)-δ13CCH4(s))⋅1/CH4(a)+δ13CCH4(s), where CH4(a) and δ13CCH4(a) are the IFAA sample values, CH4(b) and δ13CCH4(b) are the background-air values, and δ13CCH4(s) is the isotopic composition of the source.

In this study, for each source category 4 to 10 IFAA samples were collected where a single-source category contributed > 50 % of the BTF BU inventory emissions. For each category the samples were collected on different days and each day would have subtly different CH4(b) and δ13CCH4(b). Regression of a single-source data set is poorly constrained, resulting in large uncertainties in the derived δ13CCH4(s) due to the low enhancement above background (less than 0.040 ppm) and the small number of samples in each category (Appendix B). To improve the confidence in the derived δ13CCH4(s), δ13CCH4(b), and CH4(b), the Keeling model (Eq. 1) was fitted simultaneously to all source category data sets using multi-Keeling-model regression with shared parameters (CH4(b) and δ13CCH4(b)), calculated using the MultiNonlinearModelFit function in Mathematica (Version 12.0) (Wolfram Research Inc., 2019). This algorithm globally optimises δ13CCH4(s) for each category and returns the shared values for CH4(b) and δ13CCH4(b). Comprehensive details about the Mathematica MultiNonlinearModelFit function for fitting multiple data sets to multiple expressions that share parameters are available from the Wolfram function repository (Smit, 1986).

When the multi-Keeling-model regression with shared parameters is applied globally to all category data sets, the values for δ13CCH4(CSG-100to200), δ13CCH4(CSG-250to350), δ13C(Grazing-100to200), δ13CCH4(Grazing-250to350), and δ13CCH4(Feedlots-100to350) are unconstrained (allowed to vary during the regression). Background-air CH4(b) and δ13CCH4(b) are also unconstrained, and a single optimal set is determined. This assumes that CH4(b) and δ13CCH4(b) are similar on all days, which both the continuous ground surveying and airborne measurements results support (Lu et al., 2021; Neininger et al., 2021). This assumption is discussed further in Sect. 3.3.1. Because there are subtle changes in CH4(b) and δ13CCH4(b) throughout the campaign the multi-Keeling-model regression-determined values for CH4(b) and δ13CCH4(b) represent the background-air centroid for all days of measurements.

Miller and Tans (2003) discussed rearranging Eq. (1) for different data collection scenarios and regression aims. One algebraic expression rearrangement enables the source signature to be determined when CH4(b) and δ13CCH4(b) are unknown: 2δ13CCH4(a)CH4(a)=δ13CCH4(s)CH4(a)+CH4(b)(δ13CCH4(b)-δ13CCH4(s)). Like Eq. (1), when Eq. (2) is fitted to individual categories, it is poorly constrained for the dimensions of the data sets analysed.

A second algebraic expression rearrangement by Miller and Tans (2003) requires δ13CCH4(b) and CH4(b) to be specified: 3δ13CCH4(a)CH4(a)-δ13CCH4(b)CH4(b)=δ13CCH4(s)(CH4(a)-CH4(b)). For Eq. (3) CH4(b) and δ13CCH4(b) can be either constant or varying in time. A multi-Miller–Tans-model regression is equivalent to assuming constant CH4(b) and δ13CCH4(b), and under this assumption fitting either Eq. (1) or (3) using multiple regression with shared CH4(b) and δ13CCH4(b) will result in the same values being determined for the shared CH4(b) and δ13CCH4(b). Similarly, for each category almost identical values for CH4(b) and δ13CCH4(b) are determined within the precision of the simultaneous multiple regression calculations.

In Lu et al. (2021) Bayesian regression was used, and the credible interval (CrI) reported. The frequentist 95 % confidence interval (CI) is analogous to the Bayesian Crl (Lu et al., 2012; Albers et al., 2018). To allow direct comparison between this study and Lu et al. (2021), the 95 % confidence interval is reported below for δ13CCH4(s).

A subset of visually identified points of interest (1604, 1906, and 2103), all with low δ13CCH4(a) values, is analysed using the results of the multi-Keeling-model regression. Using the values for CH4(b) and δ13CCH4(b) derived from the multi-Keeling-model regression, the Keeling model (Eq. 1) is fitted to this subset to determine its δ13CCH4(s). For this subset a similar result could be obtained using Eq. (2).

In Fig. 1 the location of the IFAA samples is shown. Most of the samples were collected near or above the CSG fields. As part of the surveying on both the 16 and 18 September 2018, IFAA samples were collected remote from CSG production above the agricultural districts. Figure 3a shows that the IFAA samples were collected at two focused-altitude intervals: between 100 and 200 m a.g.l., with most IFAA samples collected at approximately 150 m a.g.l., and between 250 and 350 m a.g.l., with most samples collected at approximately 300 m a.g.l.

A plot of the BTF BU inventory emissions (kg h-1) versus IFAA sample CH4(a) (ppm) shows that there is a moderate correlation (R2=0.59) (Fig. 3b). This moderate correlation is expected because the mixing of multiple CH4 sources under turbulent atmospheric conditions is not a linear process, the inventory is calculated using annual data, and the rate of emissions for many CH4 sources in the inventory will vary either throughout the seasons (agriculture) or daily (for example, CSG production or grazing cattle location). In Fig. 3c three samples have relatively high CH4(a) values (IFAA samples 2103, 2105, and 2111), and these points are discussed in detail below. IFAA sample 1817 is highlighted, as it is discussed in Sect. 3.4.

The IFAA samples are shown in a Keeling plot (Fig. 3c). In this graph three points with relatively low δ13CCH4(a) measurements are highlighted: 1604, 1906, and 2103. These three points were not included in the initial Keeling analysis but are analysed using insights from the multi-Keeling-model regression.

The 2 h back trajectories calculated using HYSPLIT for each day are shown in Fig. A1 and for each category set in Figs. A3, A4, and A5. The total emissions from each IFAA sample's HYSPLIT BTF were determined based on the UNSW BU inventory (Neininger et al., 2021, their Supplement) and listed in column 8, Table A2. The total CH4 emissions in each IFAA sample's BTF range from 2.7 to 2209.1 kg h-1 (each BTF BU inventory is a subset of the UNSW inventory). Five source categories account for most of the CH4 emissions in the Surat Basin: CSG, feedlots, grazing cattle, piggeries, and coal mine emissions (Neininger et al., 2021). The contribution of the individual source categories to the total emissions in the BTF were calculated as outlined in Neininger et al. (2021) and are expressed as percentages of the total emissions in Fig. 4.

There are three unknown parameters in the Keeling model (Eq. 1) (δ13CCH4(s), CH4(b), and δ13CCH4(b)) and one independent variable (CH4(a) (x axis 1/CH4(a) in the Keeling plot)). To fit the Keeling model (Eq. 1) using the NonLinearModelFit and MultiNonlinearModelFit functions in Mathematica, a minimum of four IFAA samples is required (four CH4(a) and δ13CCH4(a) pairs).

For inclusion in the Keeling analysis input set for each CH4 source category, an individual source (CSG, grazing cattle, or feedlots) had to contribute > 50 % of the BTF CH4 emissions (Tables A3 and A4). The 50 % threshold was set to have enough points in each Keeling modelling set and still have one source potentially dominate the emissions. For each source category the set of samples that matched the threshold criteria is highlighted in colour in Fig. 4 and Tables A2, A3, and A4. IFAA samples excluded from the initial Keeling analysis are labelled in Fig. 4a and b. The HYSPLIT back trajectories for each IFAA sample are shown in Figs. A3, A4, and A5. These trajectories highlight that neither a single-point source nor a plume was sampled. Rather multiple plumes, where one source category dominated emissions, were analysed as a set (Fig. 4).

In Fig. 5a the result of using multi-Keeling-model regression with shared background CH4(b) and δ13CCH4(b) is shown, and the regression statistics are summarised in Table A5. Because CH4(b) and δ13CCH4(b) are shared parameters, all Keeling lines converge to a common point for background air. The resulting values of this regression for the mole fraction and isotopic composition of the background are discussed below.

In Fig. 5b the result of using multi-Miller–Tans-model regression with shared background CH4(b) and δ13CCH4(b) is shown, and the regression statistics are summarised in Table A5. As expected, these are within measurement error identical to the Keeling-model results. For this reason, the results below are discussed with reference only to the Keeling-model algebraic expression representation of the two-endmember mixing model. For the reader interested in seeing the results of fitting the Keeling (Eq. 1) and Miller–Tans (Eq. 2) models to the individual categories, they are presented in Appendix B.

In Figs. 3 and 4 IFAA samples 1604, 1906, and 2103 are identified as points of interest because they are isotopically light. These points provide unique insights into overlooked sources of CH4 in the inventory and guide where further measurements are required.

IFAA sample 1604 was collected on the western margin of the CSG field (Fig. 7). It was initially anticipated to provide a background-air reference sample, but the δ13CCH4(a) of the air sample is -47.7 ‰, which is isotopically too light for fresh air in the Surat Basin. This sample sits on a Keeling regression line with a δ13CCH4(s) of -80.2 ‰. From our current knowledge of the region this cannot be assigned to a source. The back trajectory passes over regions of mixed cropping and cattle, and -80.2 ‰ is 20 ‰ lighter than expected for cattle in the region. There is a cluster of piggeries with a holding capacity of 10 000 just outside the near-distance BTF and another piggery cluster with a holding capacity of up to 25 000 pigs immediately upwind of the 2 h BTF. However, the one reported δ13CCH4(s) signature for piggeries in Lu et al. (2021) had a value of -47.6 ‰, so piggeries are highly unlikely to be the source. There are also a few CSG production wells in the area, but this source of CH4 is isotopically too heavy. A potential source that could explain the -80.2 ‰ signature in this farming district is termites.

Upwind of IFAA sample 1906 no CH4 point source is recorded in the BU inventory (Fig. 7). There is a gravel quarry that has a small pond (200 m by 50 m) that could be a source of CH4 emissions with a biological signature. The only other known significant CH4 sources in this region are natural CH4 seeps and abandoned exploration well seeps (Lu et al., 2021). Many of these are coal exploration wells that intersect seams with a biological signature (Iverach et al., 2015; Lu et al., 2021), but these sources would be expected to have a δ13CCH4(s) signature of approximately -60 ‰, not the observed -80.2 ‰. Like sample 1604, the δ13CCH4(s) signature of -80.2 ‰ for sample 1906 could be explained by termites.

Sample 2105 (Figs. 3b and 7) is dominated by piggery emissions (56 %), which have a δ13CCH4(s) signature of -48.0 ‰ to -47.1 ‰ (CrI), with significant CSG emissions (36 %) and other minor sources (Tables A3 and A4). In Fig. 3b this point plots in a position suggesting that the inventory has underestimated emissions (Neininger et al., 2021). In Fig. 5a this point plots just above the CSG Keeling lines. A blend of piggery and CSG emissions accounts for both the relatively high CH4(a) and δ13CCH4(a). A plausible explanation for this IFAA sample is that on the day of sampling CSG emissions were higher than indicated by the BTF BU inventory. Another possibility is that the emissions arise from a closed open-pit coal mine over which the back trajectory passes. Because this coal mine is closed it is not counted in the BU inventories. Large plumes intersected near this coal mine during the ground surveying presented in Lu et al. (2021), and emissions from this recently closed coal mine may have been captured in IFAA sample 2105. An additional possibility to be explored as part of new ground surveys is the emissions from natural seeps along the Condamine River.

The two IFAA samples with the highest CH4(a) mole fraction readings were downwind of the major CSG facilities (samples 2111 and 2103, Figs. 3, 4, and 8). Sample 2103 is of particular interest because it has the lowest δ13CCH4(a) of any sample collected, and it plots on the -80.2 ‰ Keeling line in Fig. 5a. The wind was moving from southeast to northwest when samples 2103 and 2111 were collected about 20 km west–northwest of the Kenya water management ponds (Fig. 8). The back-trajectory centre line for sample 2111 passes directly over the Berwyndale South/Windbri central processing plant and Talinga plant (Fig. 8b) and immediately to the north of the Kenya water management ponds (Fig. 8c). Sample 2111 is a blended input from all these facilities. CSG sources contributed 93 % towards the CH4 emissions in the BTF BU inventory: CSG wells, 245 kg h-1; CSG raw water ponds, 787 kg h-1; CSG compressor stations, 811 kg h-1; and CSG plants, 210 kg h-1 (Table A3). Feedlot cattle contributed 4 % (88 kg h-1) and grazing cattle 3 % (64 kg h-1) (Table A4).

The back-trajectory centre line for 2103 passes over two sets of ponds: ponds near Wieambilla in the proximal BTF and further east at the Kenya water treatment complex (Fig. 8a and c). Kenya pond holds treated water suitable for adding to the Condamine River (Fig. 7). Orana 4 holds brine produced from the filtering of the raw water before being sent to the brine concentrator. Orana 2 and 3 hold water output from the brine concentrator (QGC, 2013). No plumes were sampled near this complex in Lu et al. (2021), so the δ13CCH4(s) of any emissions from these ponds is not known. CSG sources contributed 96 % towards the emissions in the BTF BU inventory for sample 2103: CSG wells, 251 kg h-1; CSG raw water ponds, 586 kg h-1; CSG compressor stations, 714 kg h-1; and CSG plants, 338 kg h-1 (Table A3).

Sample 1817 (Figs. 3c, 5a, and 8) also has a back-trajectory line that passes over the Kenya water management ponds. It was collected 35 km south of the ponds and other major CSG facilities, which accounts for its lower CH4 mole fraction. The back-trajectory centre line for 1817 passes over the easternmost Kenya water management pond, Orana 1, which is a raw water pond. CH4 emitted from this pond is likely to have a similar composition to the produced gas. CSG sources contributed 97 % of the CH4 emissions in the BTF: CSG wells, 136 kg h-1; CSG raw water ponds, 582 kg h-1; CSG compressor stations, 459 kg h-1; and CSG plants, 78 kg h-1 (Table A3). For sample 1817 there was also a minor input from grazing cattle (2.5 %; 32.7 kg h-1; Table A4). This sample does not plot as an outlier (Figs. 3c and 5a).

Samples 1817 and 2111 plot in the Keeling plot (Fig. 5a) in positions consistent with our knowledge of the δ13CCH4(s) signatures of sources in the BTF BU inventory. To explain the position of sample 2103 in Fig. 5a a source of CH4 with a δ13CCH4(s) signature of approximately -80 ‰ is required. The size and position of the Kenya water management treatment complexes associated with the water treatment, the presence of brine ponds, and other waste together make this facility a potential location for the missing source of CH4 with an δ13CCH4(s) signature of approximately -80 ‰. The back trajectory also passes over forested areas where there are termites. Further fieldwork is required to answer why sample 2103 indicates a missing biological source of CH4 in the inventories.