Table 1 lists current and scheduled satellite instruments with documented or expected capability for quantifying methane emissions, and Table 2 gives specific attributes for each. We classify the instruments as area flux mappers or point source imagers, and Fig. 1 illustrates these two fleets. Area flux mappers are designed to observe total emissions on global or regional scales with 0.1–10 km pixel size. Point source imagers are fine-pixel (<60 m) instruments designed to quantify individual point sources by imaging the plumes. Point source imagers have much finer spatial resolution than area flux mappers but lower precision.

All instruments in Table 1 except MERLIN observe methane by SWIR solar backscatter from the Earth's surface, either at 1.63–1.70 µm (1.65 µm band) or at 2.2–2.4 µm (2.3 µm band). Atmospheric scattering is weak in the SWIR except for clouds and large aerosol particles. Under clear skies, methane is observed down to the surface with near unit sensitivity (Worden et al., 2015). The retrieval may fail if the surface is too dark, such as over water or forest canopies (Ayasse et al., 2018). Observations over water can be made by sunglint when the sun–satellite viewing geometry is favorable. The MERLIN lidar instrument emits its own 1.65 µm radiation and detects the reflected signal. It can observe over water and at night, but its sensitivity and coverage are lower than for the solar backscatter instruments. Lidar capability to observe methane from space is currently limited by laser technology (Riris et al., 2019).

Not included in Table 1 are instruments that measure methane in the thermal infrared (TIR) or by solar occultation. These instruments are not sensitive to methane near the surface and are therefore not directly useful for quantifying methane emissions. TIR instruments have been used for remote sensing of methane plumes from aircraft (Hulley et al., 2016), but measurements from satellites mainly sense the upper tropospheric background (Worden et al., 2015). Solar occultation instruments such as ACE-FTS provide sensitive measurements of stratospheric methane profiles (Koo et al., 2017) but cloud interference prevents observations in the troposphere. TIR and solar occultation instruments can complement SWIR data by providing information on background methane in the upper troposphere and stratosphere (Zhang et al., 2021; Tu et al., 2022).

The spectrally resolved SWIR backscattered solar radiation detected by satellite under clear-sky conditions can be used to retrieve the total atmospheric column of methane, ΩCH4 [molecules cm-2], as will be reviewed in Sect. 2.2. To remove the variability from surface pressure, measurements are typically reported as dry column mixing ratio XCH4=ΩCH4/Ωa,d, where Ωa,d is the dry air column [molecules cm-2]. Normalizing to dry air rather than total air avoids introducing dependence on water vapor.

All instruments in Table 1 except EMIT and GeoCarb are in low-elevation polar sun-synchronous orbit and observe globally at specific local times of day, either morning or early afternoon. Morning has greater probability of clear sky, while early afternoon has steadier boundary layer winds for interpreting methane enhancements. GOSAT (2009–present) and its follow-on GOSAT-2 (2018–present) provide global coverage every 3 d for 10 km circular pixels spaced about 270 km apart, while TROPOMI (2018–present) provides full global daily coverage with 5.5×7 km2 pixels. Figure 2 shows mean TROPOMI XCH4 data for two different seasons, illustrating the dense coverage. Future instruments GOSAT-GW (2023 launch, 10×10 km2 pixels with full global coverage every 3 d in wide-swath mode), Sentinel-5 (2024 launch, 7.5×7.5 km2 pixels with full global daily coverage), and CO2M (2025 launch, 2×2 km2 pixels with full global coverage every 5 d) will continue the global observation record. MERLIN will provide day and night global coverage along its lidar orbit track. Sentinel-2 and Landsat instruments provide full global coverage with 20–30 m pixels every 5 d (Sentinel-2) or 16 d (Landsat) and can detect very large point sources over bright spectrally homogeneous surfaces. EMIT (designed to observe arid surfaces for dust generation) will be on a 51.6∘ inclined orbit aboard the International Space Station with variable local overpass times. GeoCarb will be in geostationary orbit over the Americas and will provide subdaily observations from 45∘ S to 55∘ N.

Several narrow-swath instruments in Table 1 are selective in their observations to focus on specific targets and avoid cloudy conditions. The GHGSat instruments observe selected 12×12 km2 scenes with 25×25 m2 pixel resolution and instrument pointing to increase the signal-to-noise ratio (SNR). Carbon Mapper will observe 18 km swaths with imaging strips as long as 1000 km in push-broom mode and shorter strips in target-track (instrument-pointing) mode. GHGSat has six satellites in orbit as of this writing to achieve frequent return times, and Carbon Mapper similarly plans a constellation of satellites. WorldView-3 observes scenes of dimensions up to 66.5×112 km2. MethaneSAT will observe 200×200 km2 targets in oil and gas systems and agricultural regions with 130×400 m2 pixel resolution, enabling high-resolution quantification of regional emissions as well as imaging of large point sources.

All area flux mappers in Table 1 have fine (<0.5 nm) spectral resolution to enable precise measurements of methane concentrations, traded against coarser (0.1–10 km) spatial resolution. GHGSat achieves a combination of fine spatial resolution and fine spectral resolution by instrument pointing. Most other point source imagers in Table 1 are designed to observe land surfaces, which requires fine spatial resolution (<50 m) but less stringent spectral resolution. These instruments have serendipitous capability to detect methane plumes in the broad 2.3 µm band, including hyperspectral sensors with ∼10 nm spectral resolution (PRISMA, EnMAP, EMIT; Cusworth et al., 2019) and even multispectral sensors with a single 2.3 µm channel (Sentinel-2, Landsat; Varon et al., 2021) or a few channels (WorldView-3; Sanchez-Garcia et al., 2022). Carbon Mapper will have 6 nm spectral resolution, which increases precision appreciably relative to 10 nm (Cusworth et al., 2019).

All area flux mappers in Table 1 have an open data policy allowing free access from a distribution website or from the cloud. The data are generally provided as XCH4 retrievals (Level 2 or L2). MethaneSAT will distribute its data publicly as inferred methane fluxes (L4), with the L1 and L2 data also available upon request. Data access for point source imagers is presently less straightforward. Sentinel-2 and Landsat have freely accessible channel radiance (L1) data, but users must perform their own methane retrievals and source rate estimates. GHGSat and WorldView-3 make observations at the request of paying customers, with GHGSat providing column density (L2) and source rate (L4) data and WorldView-3 providing L1 data. PRISMA and EnMAP make observations upon request from the scientific community and stakeholders, and the resulting L1 data are then freely accessible, but again users must perform their own methane retrievals. Carbon Mapper will provide open L2 and L4 data.

The “full-physics” retrieval of methane columns from satellite SWIR spectra involves inversion of the spectra with a radiative transfer model (Butz et al., 2012; Thorpe et al., 2017). It typically solves simultaneously for the vertical profile of methane concentration, the vertical profile of aerosol extinction, and the surface reflectivity. Although the vertical profile of methane may be retrieved in the inversion, there is actually no significant information on vertical gradients, and only XCH4 is reported together with an averaging kernel vector for sensitivity to the vertical profile (near unity in the troposphere). The retrieval may fail if the atmosphere is hazy or if the surface is heterogeneous or too dark. Full-physics TROPOMI retrievals in the 2.3 µm band thus have only a 3 % global success rate over land (Lorente et al., 2021a) with large variability depending on location (Fig. 2). Arid areas and midlatitudes are relatively well observed. Observations are much sparser in the wet tropics because of extensive cloudiness and dark surfaces and in the Arctic because of seasonal darkness, extensive cloudiness, and low sun angles. Observations at high latitudes are very limited outside of summer, resulting in a seasonal sampling bias.

The 1.65 µm band allows the alternative CO2 proxy retrieval, taking advantage of the adjacent CO2 absorption band at 1.61 µm (Frankenberg et al., 2005). In this method, ΩCH4 and ΩCO2 are retrieved simultaneously without accounting for atmospheric scattering, and XCH4 is then derived as 1XCH4=ΩCH4ΩCO2XCO2, where XCO2 is independently specified, typically from assimilated observations or from a global chemical transport model (Parker et al., 2020; Palmer et al., 2021). The CO2 proxy method takes advantage of the lower variability of CO2 than methane and of the low CO2 co-emission from the dominant methane sources (livestock, oil and gas systems, coal mining, landfills, wastewater treatment, rice cultivation, wetlands). It is much faster than the full-physics retrieval, achieves similar precision and accuracy (Buchwitz et al., 2015), and largely avoids biases associated with surface reflectivity and aerosols because these biases tend to cancel in the ΩCH4/ΩCO2 ratio. It is subject to errors from unresolved variability of CO2 such as in urban regions and is also subject to bias for sources that co-emit methane and CO2 such as flaring and other incomplete combustion. The GOSAT instrument operating at 1.65 µm with 10 km pixels has a 24 % success rate over land using the CO2 proxy retrieval, mainly limited by cloud cover (Parker et al., 2020).

A limitation in using the 1.65 µm band is that it is narrower, with fewer spectral features and weaker absorption than the 2.3 µm band, and it therefore requires an instrument with sub-nanometer spectral resolution (Cusworth et al., 2019; Jongaramrungruang et al., 2021). The 2.3 µm band can be successfully sampled for a full-physics retrieval by hyperspectral instruments with ∼10 nm spectral resolution (Thorpe et al., 2014, 2017; Cusworth et al., 2021a; Borchardt et al., 2021; Irakulis-Loitxate et al., 2021). Precision improves with spectral resolution (Cusworth et al., 2019; Jongaramrungruang et al., 2021) and with spectral positioning relative to the methane absorption lines (Scaffuto et al., 2021). Multispectral instruments with one or several broadband channels (∼100 nm bandwidth) do not allow a spectrally resolved retrieval, but a simple Beer's law retrieval of the methane column enhancement in a plume relative to background can still be achieved in the 2.3 µm band by inferring surface reflectivity from adjacent bands or from views of the same scene when the plume is absent (Varon et al., 2021; Sanchez-Garcia et al., 2022).

Yet another approach for retrieving methane enhancements from point sources is the matched-filter method in which the observed spectrum is fitted to a background spectrum convolved with a target methane absorption spectrum capturing the 2.3 µm absorption band (Thompson et al., 2015; Foote et al., 2020). Matched filter methods have been extensively used for mapping methane point sources from airborne hyperspectral campaigns (Frankenberg et al., 2016; Duren et al., 2019; Cusworth et al., 2021b) and have also been used for satellite retrieval of point sources (Thompson et al., 2016; Guanter et al., 2021; Irakulis-Loitxate et al., 2021). These methods directly retrieve the methane enhancement above background and are faster than a full-physics retrieval. They are well-suited methods for plume imaging, where the methane enhancement above local background is the quantity of interest.

Retrievals of XCH4 may be affected by random error (precision) and systematic error (bias or accuracy). A uniform bias is inconsequential because it can be simply subtracted. Random error is reducible by temporal averaging if the observation density is high. The most pernicious error is spatially variable bias, often called relative bias (Buchwitz et al., 2015), which is generally caused by aliasing of surface reflectivity spectral features into the methane retrieval. Variable bias corrupts the retrieved concentration gradients and produces artifact features that may be wrongly attributed to methane.

Area flux mapper instruments are generally validated by reference to the highly accurate XCH4 measurements from the worldwide Total Carbon Column Observing Network (TCCON) of ground-based sun-staring spectrometers (Wunch et al., 2011). Variable bias can be estimated as the spatial standard deviation across TCCON sites of the temporal mean bias (Buchwitz et al., 2015). Schneising et al. (2019) inferred in this manner a global bias of -1.3 ppb for the TROPOMI University of Bremen methane retrieval, a precision of 14 ppb, and a variable bias of 4.3 ppb. Lorente et al. (2021a) inferred a global mean bias of -3.4 ppb and a variable bias of 5.6 ppb for the current TROPOMI version 2 Netherlands Institute for Space Research (SRON) operational retrieval. Figure 3 places these values in the context of TROPOMI observations over the Permian Basin oil field in Texas and New Mexico. A typical single day of TROPOMI observations shows large areas of missing and noisy data, and thus temporal averaging is necessary, which also reduces the random error. Averaging TROPOMI observations over a month shows full coverage of the Permian with enhancements of ∼50 ppb over the principal areas of oil and gas production, well above the variable bias of the instrument.

Reliance on the TCCON network to diagnose variable bias is limited by the sparsity of network sites, almost all of which are at northern midlatitudes. An alternative way is by reference to GOSAT. The current version 9 GOSAT retrieval using the CO2 proxy method has a variable bias of only 2.9 ppb referenced to TCCON and is recognized as a well-calibrated measurement (Parker et al., 2020). Spatial variability in the mean TROPOMI–GOSAT difference provides a global assessment of TROPOMI variable bias (Qu et al., 2021). Results in Fig. 2 (bottom panel), after correcting for a global mean TROPOMI–GOSAT difference of -10.5 ppb (TROPOMI lower than GOSAT), show that TROPOMI variable biases can exceed 20 ppb in some regions. The reason for such large biases relative to GOSAT is TROPOMI's coarser spectral sampling of the SWIR region, as well as the unavailability of the CO2 proxy retrieval at 2.3 µm. Comparing TROPOMI and GOSAT observations for a region of interest is good practice before interpreting TROPOMI data for that region (Z. Chen et al., 2022).

Variable bias is also a concern for point source imagers, where it manifests as artifact features that could be mistaken for methane plumes (Ayasse et al., 2018). This is of particular concern for heterogeneous surfaces (Cusworth et al., 2019). Artifacts can be screened by visual inspection of the candidate plumes in relation to wind direction, known infrastructure, and surface reflectivity (Guanter et al., 2021). Machine-learning methods can also be trained to detect plumes and recognize artifact noise patterns (Jongaramrungruang et al., 2022). Figure 3 shows illustrative observations of point sources from Sentinel-2, PRISMA, and GHGSat in the Permian Basin. The observations have lower precision than TROPOMI (Table 1), but the methane enhancements are much larger because the pixels are smaller. Point source detection thresholds and their relationship to precision are discussed in Sect. 5.

Global observation of methane targets the central question of why atmospheric methane has almost tripled since pre-industrial times and why it continues to increase. Ground network measurements such as from NOAA are the reference for observing global trends because of their high accuracy (Bruhwiler et al., 2021), and some sites include isotopic or other information to separate contributions from different source sectors (Lan et al., 2021). But satellites have an essential role to play because of their dense and global coverage. They can identify the regions that drive the global trend (Zhang et al., 2021). They have a unique capability to evaluate the accuracy and trends of methane emissions reported by individual countries to the UNFCCC (Janardanan et al., 2020) and thus contribute to the transparency framework of the Paris Agreement (Deng et al., 2022; Worden et al., 2022).

Global observation of methane from space is presently available from GOSAT and TROPOMI. GOSAT provides a continuous and well-calibrated record going back to 2009 (Parker et al. 2020). Inversions of GOSAT data have been used to attribute the contributions of different source regions and sectors to the methane increase over the past decade (Maasakkers et al., 2019; Chandra et al., 2021; Palmer et al., 2021; Zhang et al., 2021). The TROPOMI data stream begins in May 2018 and is much denser than GOSAT, but the ability to use TROPOMI data in global inversions is presently limited by large variable biases in some regions of the world (Qu et al., 2021; Fig. 2). This is likely to improve with future retrieval versions and may be overcome with careful data selection. Continuity of global methane observations from space is expected over the next decade with the GOSAT series (GOSAT-2, GOSAT-GW), Sentinel-5, and CO2M (Table 1). MERLIN could make an important contribution toward better understanding of methane emissions in the Arctic, which is otherwise difficult to observe from space.

There is considerable interest in using satellite observations to quantify methane emissions with high resolution on regional scales. This is important for reporting of emissions at the national or sub-national state level, for monitoring oil and gas production basins, and for separating contributions from different source sectors. Oil and gas production basins are typically a few hundred kilometers in size and may contain thousands of point sources that are individually small but add up to large totals and are best quantified on a regional scale (Lyon et al., 2015). Several field campaigns using surface and aircraft measurements have targeted oil and gas fields in North America (Karion et al., 2015; Pétron et al., 2020; Lyon et al., 2021), but these campaigns are necessarily short and are not practical in many parts of the world.

TROPOMI with its 5.5×7 km2 pixel resolution and global continuous daily coverage is presently the only satellite instrument capable of high-resolution regional mapping of methane emissions. GOSAT data are too sparse. TROPOMI has been used to quantify emissions from oil and gas production fields including the Permian Basin (Zhang et al., 2020), other fields in the US and Canada (Shen et al., 2022), and the Mexican Sureste Basin (Shen et al., 2021), revealing large underestimates in the bottom-up inventories. It has also been used to quantify total methane emissions from China and to attribute them to source sectors (Z. Chen et al., 2022). The variable bias problems that affect global TROPOMI inversions can be less problematic on the scale of source regions where methane enhancements are large, the bias may be less severe (Fig. 2), and bias correction is possible through adjustment of boundary conditions in the transport model (Shen et al., 2021). Capability for regional mapping of methane emissions is expected to greatly expand in the future with the MethaneSAT, GOSAT-GW, Sentinel-5, and CO2M instruments.

Monitoring large point sources is important for reporting of emissions, and detection of unexpectedly large point sources (super-emitters) can enable prompt corrective action. In situ sampling and remote sensing from aircraft has been used extensively to quantify point sources (Frankenberg et al., 2016; Lyon et al., 2016; Duren et al., 2019; Hajny et al., 2019; Y. Chen et al., 2022; Cusworth et al., 2022) but is limited in spatial and temporal coverage. Satellites again have an essential role to play. They have enabled the discovery of previously unknown releases (Varon et al., 2019; Lauvaux et al., 2022) and the quantification of time-integrated total emissions from gas well blowouts (Cusworth et al., 2021a; Maasakkers et al., 2022a).

Observing point sources from space has unique requirements. Plumes are typically less than 1 km in size (Frankenberg et al., 2016; Fig. 3), thus requiring satellite pixels finer than 60 m (Ayasse et al., 2019). It is desirable to quantify emissions from single overpasses, though temporal averaging of plumes to improve SNR is possible with wind rotation if the precise location of the source is known (Varon et al., 2020). The emissions are temporally variable, motivating frequent revisit times that can be achieved by a constellation of instruments. On the other hand, precision requirements are less stringent than for regional or global observations because of the larger magnitude of the concentration enhancements.

The potential for space-based land imaging spectrometers to detect methane point sources was first demonstrated with the hyperspectral Hyperion instrument for the Aliso Canyon blowout (Thompson et al., 2016). Hyperspectral sensors such as PRISMA and others of similar design have since proven capable of quantifying point sources of ∼500 kg h-1 (Cusworth et al., 2021a; Guanter et al., 2021; Irakulis-Loitxate et al., 2021; Nesme et al., 2021). The first satellite instrument dedicated to quantifying methane point sources was the GHGSat-D demonstration instrument launched in 2016 with 50×50 m2 effective pixel resolution and a precision of 12 %–25 % depending on surface type (Jervis et al., 2021). Varon et al. (2019) demonstrated the capability of that instrument for discovering and quantifying persistent point sources in the range 4000–40 000 kg h-1 in an oil and gas field in Turkmenistan. Five follow-up GHGSat instruments with precisions of 1 %–2 % were subsequently launched in 2020–2022, building up to a constellation with frequent return times.

Multispectral instruments such as Sentinel-2, Landsat, and WorldView-3 are also capable of detecting and quantifying very large point sources (Varon et al., 2021; Ehret et al., 2022; Sanchez-Garcia et al., 2022; Irakulis-Loitxate et al., 2022a). Sentinel-2 and Landsat provide global and freely accessible data that could form the foundation of a global detection system for super-emitters (Ehret et al., 2022). A large-scale survey of point emissions across the western coast of Turkmenistan was achieved with the combination of Sentinel-2 and Landsat (Irakulis-Loitxate et al., 2022a).

Detection of methane plumes from space has mainly been over bright land surfaces. Observation of offshore plumes such as from oil and gas extraction platforms is more difficult because of the low reflectance of water in the SWIR. The signal can be enhanced by observing in the sunglint mode, in which the sensor captures the solar radiation specularly reflected by the water. The sunglint observation configuration can be achieved by agile platforms able to point in the Sun-surface forward scattering direction (PRISMA, Worldview-3, GHGSat, Carbon Mapper) or by instruments with a field-of-view sufficiently large that part of the swath falls in the forward scattering area (TROPOMI, Sentinel-2, Landsat). Irakulis-Loitxate et al. (2022b) demonstrated the ability of sunglint retrievals from WorldView-3 and Landsat-8 to detect large plumes from offshore platforms in the Gulf of Mexico.

The capability to monitor methane point sources from space is expected to expand rapidly in coming years through the GHGSat and Carbon Mapper constellations as well as new hyperspectral missions (Cusworth et al., 2019). Expanding constellations observing with frequent return times and at different times of day will enable better understanding of the intermittency of methane emissions. In an aircraft survey of the Permian Basin, Cusworth et al. (2021b) found that individual point sources produced detectable emissions only 26 % of the time on average. Similar intermittency was observed for oil and gas facilities in California (Duren et al., 2019). Allen et al. (2017) and Vaughn et al. (2018) point out that some emissions from the oil and gas infrastructure are highly intermittent by design (liquids unloading, blowdowns, and startups) and may have predictable diurnal variations. Emissions due to equipment failure may be persistent (leaks, unlit flares), sporadic (responding to gas pressure), or single events (accidents). An increased frequency of observation can identify persistence of emissions to enable corrective action, and better understanding of point sources that are intermittent by design can lead to better quantification of time-averaged emissions. Beyond this short-term intermittency, there is also long-term variability related to operating practices and facility life cycle (Cardoso-Saldaña and Allen, 2020; Johnson and Heltzel, 2021; Varon et al., 2021; Allen et al., 2022; Ehret et al., 2022), stressing the importance of sustained long-term monitoring.

Area flux mappers produce 2-D fields of methane observations from which to optimize 2-D fields of gridded emission fluxes. The optimization involves an atmospheric transport model (forward model) to relate emissions to the observed concentrations. The optimal emissions are generally obtained by Bayesian inference, fitting the observations to the forward model and including prior estimates of emissions to regularize the solution where the observations provide insufficient information (Brasseur and Jacob, 2017). Optimizing temporal trends of emissions can be done as part of the solution or sequentially using a Kalman filter (Feng et al., 2017).

The basic procedure is as follows. Given an ensemble of observations over a domain of interest assembled in an observation vector y, the task is to optimize the distribution of emission fluxes assembled in a state vector x of dimension n. The relationship between x and y can be assumed linear for methane, despite the sensitivity of OH concentrations to methane concentrations. This is because the inversion does not significantly change the global methane concentration, which is set by observation; furthermore, for regional inversions, the timescale for ventilation of the regional domain is much shorter than that for chemical loss. Global inversions often optimize OH concentrations as part of the state vector and that relationship can also be assumed linear. Further assuming Gaussian error probability density functions (pdfs) for x and y, the optimal (posterior) estimate of x is obtained by minimizing a Bayesian cost function J(x) of the form (Brasseur and Jacob, 2017): 2J(x)=(x-xA)TSA-1(x-xA)+γ(y-Kx)TSO-1(y-Kx), Here xA is the prior estimate of emissions, SA is the corresponding prior error covariance matrix, K=∂y/∂x is the Jacobian matrix describing the sensitivity of observations to emissions as given by the atmospheric transport model, SO is the observational error covariance matrix including contributions from instrument and transport model errors, and γ is a regularization parameter that may be needed to correct overfit caused by imperfect definition of SO (Lu et al., 2021). Since the relationship between x and y is linear, K fully defines the atmospheric transport model for the inversion. Jacob et al. (2016) describe alternative formulations for the cost function such as in geostatistical inverse modeling where prior information is provided as the relative spatial distribution of emissions rather than emission magnitudes (Miller et al., 2020).

Specification of the error covariance matrices SA and SO strongly affects the solution. Construction of SA can be done by intercomparing bottom-up inventories (Maasakkers et al., 2016; Bloom et al., 2017) or by using error estimates generated by the bottom-up inventories (Scarpelli et al., 2020). Construction of SO can be done by the residual error method in which the observations are compared to simulated concentrations from the atmospheric transport model with prior emission estimates, and the residual difference after removing the mean bias is taken to be the observational error (Heald et al., 2004; Wecht et al., 2014). The observational error for satellites is generally found to be dominated by the instrument retrieval error rather than by the transport model error, whereas for in situ observations it is dominated by the transport model error (Lu et al., 2021).

Minimization of the cost function J(x) in Eq. (2) to obtain the posterior solution x^ and its error covariance matrix S^ can be done either numerically or analytically (Brasseur and Jacob, 2017). S^ and the related averaging kernel matrix A=∂x^/∂x=In-S^SA-1 (Rodgers, 2000) determine the information content from the observations and the ability of the inversion to improve on the prior estimate. The diagonal terms of A ranging from 0 to 1 are called the averaging kernel sensitivities and measure the ability of the observations to constrain the solution for that state vector element independently of the prior estimate (1= fully, 0= not at all). The trace of A is called the degrees of freedom for signal (DOFS) and represents the total number of pieces of information that can be fully constrained from the observations. An inherent assumption is that the observations, the transport model, and the prior information are unbiased. Although the prior estimate is in principle unbiased since it represents our best estimate before the observations are taken, under-accounting of SA together with incorrect spatial distribution of prior emissions can drive bias in inversion results (Yu et al., 2021).

Numerical solution for min(J(x)) using the adjoint of the atmospheric transport model or other variational methods optimizes a state vector of any dimension by avoiding explicit construction of the full Jacobian matrix K and may use various procedures to estimate S^ (Bousserez et al., 2015; Cho et al., 2022). Analytical solution provides a closed-form expression for S^ but requires the computationally expensive construction of K column-by-column with n perturbation runs of the atmospheric transport model. This limits the dimension and hence the resolution of the state vector that can be optimized. However, once K has been constructed, inversion ensembles can be conducted at no significant added computational cost to explore uncertainties in inversion parameters or to examine the complementarity and consistency of different observation subsets such as from different satellite instruments or from ground-based sites (Lu et al., 2021, 2022). This includes optimization of the regularization parameter γ so that the sum of prior terms in the posterior cost function matches the expected value from the chi-square distribution, JA(x^)=(x^-xA)TSA-1(x^-xA)∼n (Lu et al., 2021). Increasing access to large computational clusters has facilitated the construction of K as an embarrassingly parallel problem, enabling analytical solution for state vectors with n>1000 (Maasakkers et al., 2019). Nesser et al. (2021) show that even larger dimensions can be accessed by approximating the Jacobian along leading patterns of information content.

Figure 5 illustrates the inversion of TROPOMI observations with a 1-month example for the Permian Basin using an analytical solution with 0.25∘×0.3125∘ (≈25×25 km2) resolution. This calculation was done on the Amazon Web Services (AWS) cloud with the Integrated Methane Inversion (IMI) open-access facility for analytical inversions of TROPOMI data, enabling users to directly access the TROPOMI data archived on AWS and infer emissions for their selected domain and time window of interest with pre-compiled inversion code (Varon et al., 2022).

The assumption of Gaussian error pdfs for prior emission estimates in Eq. (2) may not always be appropriate. A log-normal distribution is often more correct (Yuan et al., 2015) and can be accommodated in analytical inversions (Maasakkers et al., 2019; Z. Chen et al., 2022). Brandt et al. (2016) show that the log-normal distribution still underestimates the heavy tail of the frequency distribution of point sources (the super-emitters). Application of inverse methods to detect and quantify individual super-emitters within a source region (such as an oil and gas field) may require a bimodal pdf for prior estimates, and an L1 norm cost function may be better suited than the standard L2 norm of Eq. (2) (Cusworth et al., 2018). A Markov chain Monte Carlo (MCMC) method for the inversion as used by Western et al. (2021) enables the specification of any prior and observational error pdfs and returns the full posterior error pdf on emissions, but it is computationally expensive and its cost increases rapidly as n increases.

The inversion typically optimizes a geographical 2-D array of emission fluxes, but quantifying emissions by source sector is often of ultimate interest. Sectoral information is generally contained in the prior inventory. The simplest approach is to assume that the posterior-to-prior emissions ratio for a given grid cell applies equally to all emissions in that grid cell (Turner et al., 2015) or in a manner weighted by the prior uncertainties of the different sectors (Shen et al., 2021). The posterior error covariance matrix S^ and averaging kernel matrix A on the 2-D grid can similarly be mapped to specific sectors and/or be summed over a domain such as an individual country (Maasakkers et al., 2019). A more general approach for sectoral attribution introduced by Cusworth et al. (2021c) maps the (x^, S^) solution onto any alternative state vector z (such as sector-resolved emissions) with its own prior information (zA, ZA) to obtain a solution z^ with posterior error covariance matrix Z^. This specifically allows for comparisons of results from inversions using different prior information.

Quantification of point sources from satellite observations of instantaneous plumes poses a different kind of inversion problem. In this case, a single quantity, the point source rate Q [kg s-1], is to be inferred from a single observation of the plume. Figure 3 showed examples of plume observations. The morphology of the instantaneous plume is determined by turbulent diffusion superimposed on the mean wind, with a plume boundary (commonly called the plume mask) defined by the detection limit of the instrument. The observation is of the total methane column and so is relatively insensitive to vertical boundary layer mixing, which is a major source of error in interpreting plumes from in situ aircraft observations (Angevine et al., 2020). On the other hand, unlike for in situ aircraft observations, there is no direct measurement of the wind speed U in the plume. The lack of precise wind speed information is a major source of error for interpreting satellite observations because concentrations in the plume vary as the ratio Q/U, meaning that errors in U propagate proportionally to errors in Q.

Figure 6 summarizes different methods for inferring point source rates from satellite observations of instantaneous plumes. Details on these methods are given by Krings et al. (2011), Varon et al. (2018), and Jongaramrungruang et al. (2019, 2022). The Gaussian plume is the classic model for turbulent diffusion from a point source, but it is valid only for a plume sampling a representative ensemble of turbulent eddies. Methane plumes are generally too small for this condition to be met (Jongarangmrungruang et al., 2019), as illustrated in Fig. 3 where the plume shapes are not Gaussian. A simple mass balance method applying the local wind speed to the methane enhancement observed in the plume is flawed for sub-kilometer scales because ventilation is determined by turbulent eddies more than by the mean wind (Varon et al., 2018).

The Gauss theorem method, in which the source rate is calculated as the outward flux summed along a contour surrounding the point source, is extensively used for in situ aircraft observations where concurrent measurements of wind vector and methane concentration are available to calculate the local flux as the aircraft circles around the source (Hainy et al., 2019). In the absence of in situ wind data, one can apply a single estimate of the wind vector based on local station or assimilated data (Krings et al., 2011). However, the calculation then does not account for the contribution of turbulent diffusion to the outward flux. In addition, any sources within the contour will alias into the inferred point source rate.

Two successful methods to derive point source rates from observations of instantaneous plumes have been the cross-sectional flux (CSF) method (White, 1976; Krings et al., 2011), in which the source rate is inferred from the product of the methane enhancement and the wind speed integrated across the plume width, and the integrated mass enhancement (IME) method (Frankenberg et al., 2016; Varon et al., 2018), in which the total mass enhancement in the plume is related to the magnitude of emission with a parameterization dependent on wind speed. Both methods are widely applied to the retrieval of point source rates from satellite observations and they yield consistent results (Varon et al., 2019). The CSF method is more physically based, and source rates can be derived from cross sections at different distances downwind to reduce error (Fig. 6). The contribution of turbulent diffusion to the flux can be neglected in the direction of the wind following the slender plume approximation (Seinfeld and Pandis, 2016). However, the dependence on wind direction is an additional source of error relative to the IME method.

Both the CSF and IME methods require estimates of wind speed relevant to plume transport. For the CSF method this is the mean wind speed over the vertical depth of the plume, which can be parameterized from the 10 m wind speed (Varon et al., 2018) or interpolated from a database of wind speed vertical profiles (Krings et al., 2011). The effective wind speed Ueff in the IME method accounts for the effect of turbulent diffusion in plume dissipation and can be parameterized as a function of an observable 10 m wind speed by using large-eddy simulations (LES) of synthetic plumes sampled with the instrument pixel resolution, plume mask definition, and observing time of day (Varon et al., 2018). The need for independent information on wind speed, either from measurements at the point source location or from a meteorological database, can dominate the error budget in inferring source rates from the CSF and IME methods, and typically limits the precision to 30 % (Varon et al., 2018). The error is larger for weak winds, which tend to be more variable and smaller for strong steady winds. However, plumes are less likely to be detectable in strong winds because of dilution. Weak winds are thus favorable for plume detection but can induce large error in source quantification.

Jongaramrungruang et al. (2019) showed that the morphology of an observed plume contains information on wind speed, as long slender plumes are associated with high wind speeds while short stubby plumes are associated with low wind speeds. By using the plume angular width as a measure of wind speed, they were able to infer source rates without independent wind information. Jongaramrungruang et al. (2022) developed that idea further with a convolutional neural network (CNN) approach trained on LES plume images to learn the source rate from the 2-D plume structure. Application to synthetic plumes, as would be sampled by the AVIRIS-NG aircraft instrument at 1–5 m pixel resolution, showed a mean precision of 17 % and a detection threshold of 50 kg h-1 over spectrally homogeneous surfaces. This method has not yet been applied to satellite observations where coarser pixels would result in lower sensitivity and where retrievals are more subject to artifacts.

Here we examine the ability of area flux mappers to detect total methane emission fluxes from a target domain with a desired spatial resolution. This can involve repeated observations of the domain over multiple passes to increase precision and observation density, as illustrated in Fig. 3. The observation time required to detect a desired flux threshold at a desired spatial resolution then depends on the instrument precision, the spatial coverage, the fraction of successful retrievals, the pixel size, the variability of emissions, and the return time.

Following the conceptual model of Jacob et al. (2016), the methane column enhancement ΔX [ppb] resulting from a uniform emission flux E [kg km-2 h-1] over a square domain of dimension W [km] is given by 3ΔX=αEW, with a scaling coefficient α=(Ma/MCH4)g/pU where Ma and MCH4 are the molecular weights of dry air and methane, g is the acceleration of gravity, p is the surface pressure, and U is the wind speed for ventilation of the domain. With the units above and assuming p=1000 hPa and U=5 km h-1, we have α=4.0×10-2 ppb km h kg-1. An instrument with pixel-level precision σI [ppb] can detect this emission flux with a single measurement if ΔX>>σI, but this is often not the case. Spatial and temporal averaging of observations improves the effective precision, and this improvement goes as the square root of the number of observations if the error is random, uncorrelated, and representatively sampled (IID conditions). The time required for detecting the mean emission flux E over a domain of dimension W with a signal-to-noise ratio of 2 is then given by 4t=tRmax⁡1,1FNmax1,2σΔX2, where tR is the return time of the instrument (time interval between successive passes), N is the number of observations within the domain per individual pass for instrument pixel sizes D smaller than W (for continuous mapping and square pixels, we have N=(W/D)2), F is the fraction of successful retrievals, and σ [ppb] is the variability that results from both the instrument precision and the spatial variability σX (D,W) of the enhancement ΔX sampled by the pixels within the domain: 5σ=σI2+σX(D,W)2. Equations (3)–(5) provide a simple conceptual framework for evaluating the ability of area flux mappers to detect regional emissions of a certain magnitude and with a desired spatial resolution. For illustration purposes, consider an objective to detect emissions at either 100 or 10 km resolution. In the gridded version of the methane emission inventory from the US Environmental Protection Agency (Maasakkers et al., 2016), 75 % of total national anthropogenic emissions are contributed by 0.1∘×0.1∘ (≈10×10 km2) grid cells with emission flux E>0.5 kg km-2 h-1, and 30 % are contributed by grid cells with E>5 kg km-2 h-1 (Jacob et al., 2016). Shen et al. (2022) find a mean emission of 0.18 Tg yr-1 for 12 major oil and gas production basins in the US EPA inventory, which for a typical basin scale of 200×200 km2 corresponds to a mean emission flux of 0.5 kg km-2 h-1. Taking E=0.5 kg km-2 h-1 as a desired flux detection threshold on a 100 km scale, or alternatively E=5 kg km-2 h-1 as a desired flux detection threshold on a 10 km scale, we find from Eq. (3) a mean enhancement ΔX=2.0 ppb. Instrument precisions for the flux mappers in Table 1 are in the range 3–15 ppb, and we assume that σX is small in comparison. We further assume F=0.24 for instruments operating at 1.65 µm by analogy with GOSAT using the CO2 proxy method (mainly limited by cloud cover) and F=0.03 for instruments operating at 2.3 µm by analogy with TROPOMI (limited by both cloud cover and spectrally inhomogeneous surfaces). Other instrument properties are taken from Table 1.

Table 3 shows the results of this illustrative calculation. In the 100 km resolution case we find that TROPOMI requires a 4-week averaging period, limited by the small fraction of successful retrievals. GOSAT-GW requires 18 d in global viewing mode, as the greater fraction of successful retrievals is offset by coarser pixels and 3 d return time. It requires only one pass in target mode. MethaneSAT requires a single pass and is limited by its 3 d return time. Sentinel-5 requires 5 d, much shorter than TROPOMI despite coarser pixels because it uses the 1.65 µm band. GeoCarb requires only 3 d because of its twice-daily observations. CO2M requires only a single pass and is limited by its 5 d return time. In the 10 km resolution case, we find that only MethaneSAT has an averaging time of less than a week, with GOSAT-GW requiring 18 d in target mode (limited by its lower instrument precision) and other instruments requiring several months or more. However, both MethaneSAT and GOSAT-GW in target mode only cover limited domains (200×200 km2 for MethaneSAT).

The above conceptual model is crude and overoptimistic, assuming ideal reduction of errors and uncorrelated retrieval success across instrument pixels, ignoring variable bias, and taking instrument specifications from Table 1 at face value, but it is useful for intercomparing instruments and it highlights critical variables determining detection thresholds for different applications. The advantage of the 1.65 µm band is readily apparent because it achieves a much higher success rate through the CO2 proxy retrieval. The MethaneSAT instrument with high precision and small pixels is most useful for quantifying fluxes at high spatial resolution. For coarser resolutions, return time and spatial coverage can be more important considerations.

In the case of point source imagers, the detection threshold applies to single-pass observations of the plumes. Table 4 lists point source detection thresholds reported in the literature for different instruments. Detection thresholds are defined by the ability to determine the plume mask against a noisy background and to retrieve the corresponding emissions. The detection thresholds for a given instrument depend strongly on surface type and are lowest for bright, spectrally homogeneous surfaces. They also depend on wind speed, which complicates the definition of detection threshold because weak winds facilitate detection but cause large error in quantification (Varon et al., 2018). The best range of wind speeds to allow both detection and quantification is 2–5 m s-1 (Varon et al., 2018). Sherwin et al. (2022) conducted a series of controlled release experiments under those favorable surface and wind conditions and confirmed the ability of GHGSat to quantify emissions down to 200 kg h-1 and Sentinel-2, Landsat-8, PRISMA, and WorldView-3 to quantify emissions down to the 1400–4000 kg h-1 range.

For a given surface and wind speed, the main instrument predictors of point source detection threshold are spatial resolution, spectral resolution, and precision. Finer spatial resolution decreases the dilution of the plume enhancements over the pixel area, thus increasing the magnitude of the enhancements within plume pixels and facilitating detection. An airborne imaging spectrometer observing from low altitude such as AVIRIS-NG (with spatial resolution of 1–8 m depending on aircraft altitude) is thus much more sensitive than satellite instruments with similar spectral resolution. Higher spectral resolution increases precision and reduces the aliasing of surface spectral features into the methane retrieval (Cusworth et al., 2019; Jongaramrungruang et al., 2021). For hyperspectral and multispectral instruments, the spectral positioning of the bands relative to the methane absorption lines is also important (Scaffuto et al., 2021; Sanchez-Garcia et al., 2022). Precision depends on other instrument properties beyond spectral resolution and positioning, including the capability of pointing to specific targets to increase the SNR through longer sample collection. Pointing is how GHGSat achieves a combination of high spatial and spectral resolution.

The detection thresholds in Table 4 are not strictly comparable between instruments because they reflect different levels of evidence. One may still usefully classify the instruments by order-of-magnitude thresholds of ∼100, ∼500, and ∼1000–10 000 kg h-1 (Fig. 4). Instruments in the ∼100 kg h-1 class include GHGSat, WorldView-3, and Carbon Mapper. A typical point source imager with spatial resolution ∼30 m requires spectral resolution of 5 nm or better to fit into this class (Cusworth et al., 2019), though WorldView-3 can achieve this class for bright spectrally homogeneous surfaces through its combination of very high spatial resolution (3.7×3.7 m2) and favorable spectral positioning (Sanchez-Garcia et al., 2022).

Instruments in the ∼500 kg h-1 class include the land hyperspectral sensors (PRISMA, EnMAP, EMIT) and MethaneSAT. The land hyperspectral sensors have ∼30 m spatial resolution and achieve this class with 10 nm spectral resolution in the 2.3 µm band, enabling either a full-physics or matched filter retrieval. MethaneSAT will have coarser 130×400 m2 spatial resolution but higher precision enabled by 0.3 nm spectral resolution in the 1.65 µm band, with the added benefit of allowing a CO2 proxy retrieval to minimize artifacts.

Instruments in the 1000–10 000 kg h-1 class include the multispectral land sensors Sentinel-2 and Landsat with 20–30 nm spatial resolution and a single measurement in the 2.3 µm band to allow a simple Beer's law retrieval. TROPOMI can detect extremely large point sources or clusters of sources (>25000 kg h-1) over its 5.5×7 km2 pixels (Lauvaux et al., 2022), though coarse spatial resolution hinders source identification.

The relevance of measuring individual point sources at these different thresholds can be assessed by considering their contributions to total emissions. Cusworth et al. (2022) find on average that 40 % of emissions from US oil and gas fields originate from point sources >10 kg h-1 detectable by AVIRIS-NG. Figure 7 shows the cumulative frequency distributions (CFDs) by number and total emission of point sources larger than 10 kg h-1 sampled by airborne remote sensing over California and over US oil and gas fields (Duren et al., 2019; Cusworth et al., 2022). Results are shown for individual campaigns and for the combined CFD with equal weighting between campaigns. A satellite instrument with detection threshold of 100 kg h-1 could detect 50 %–95 % of point sources depending on the region (80 % in the combined data set), contributing 75 %–99 % of point source emissions (95 % for the combined data set). An instrument with detection threshold of 1000 kg h-1 could detect 0 %–15 % of point sources (5 % for the combined data set), contributing 0 %–55 % of point source emissions (30 % in the combined data set). Brandt et al. (2016) find that sources in the 10–100 kg h-1 range contribute 20 % of emissions from point sources >10 kg h-1 in their survey of emissions from US oil and gas fields. The data set of Fig. 7 includes only a few emitters in the ∼ 10 000 kg h-1 range. Global statistics of aircraft and satellite data suggest a power law frequency distribution of point source emissions with ∼100× fewer sources at 10 000 kg h-1 than at 1000 kg h-1 (Ehret et al., 2022; Lauvaux et al., 2022). These so-called ultra-emitters could still contribute significantly to total emissions in some regions.

Observations from area flux mappers are generally used to infer 2-D distributions of total emissions over a regional domain of interest by Bayesian inference. The observing system completeness is then defined by the DOFS (Sect. 4.1 and Fig. 5). Given n state vector elements of emissions on the 2-D grid, the DOFS tell us how many of those elements are quantified by the observations, and the averaging kernel sensitivities (diagonal terms of the averaging kernel matrix, adding up to the DOFS) give that information for the individual state vector elements.

As pointed out by Nesser et al. (2021) and Varon et al. (2022), it is possible to roughly estimate the DOFS of an observing system for a selected domain and time period without doing any actual forward model calculations. Consider a domain divided into n emission state vector elements of individual dimension W [km], sampled with an instrument providing m successful observations over the domain in the selected time period. Let σA be the mean prior error standard deviation for the individual state vector elements and σO the mean observational error standard deviation. The DOFS can then be estimated as 6DOFS=nσA2σA2+(σO/k)2m, where k=ΔX/E [ppb km2 h kg-1] is the Jacobian matrix element that relates the column mixing ratio enhancement ΔX [ppb] over a state vector element to the emission flux E [kg km-2 h-1] for that element. Following Nesser et al. (2021), we can approximate k with a simple mass balance model as 7k=ηMaMCH4WgUp, where η is a coefficient to account for turbulent diffusion. Nesser et al. (2021) and Varon et al. (2022a) find that η=0.4 is a suitable value for W in the range 25–100 km. Further assuming U=5 km h-1 and p=1000 hPa, we obtain k=1.4×1010W [ppb km2 h kg-1]. The mean prior error standard deviation can be estimated as σA=fQA/(nW2), where QA is the total prior estimate of emission in the domain [kg h-1] and f is the fractional error (such as 50 %). For the example of Fig. 5 with a 1-month inversion of TROPOMI observations over the Permian Basin, Varon et al. (2022) find that this rough estimate prior to doing the inversions yields a DOFS of 11.7, close to the value of 10.8 found in the actual inversion.

The simple estimate of DOFS in Eq. (6) yields basic insights into the factors affecting observing system completeness for an area flux mapper. Instrument precision and number of observations (or observation density for a given area) are critical. The bar for the observations to improve on the prior estimate depends on the estimated error for that prior estimate (smaller prior error means a higher bar for the observations). Increasing the requirement on spatial resolution (large n, small W) leads to smaller absolute prior errors for individual state vector elements and in turn raises the requirement on the precision and number of observations.

Observing system completeness for a point source imager (or a constellation) can be defined as its ability to quantify total emissions from point sources larger than 10 kg h-1 over a selected domain and time window. Such completeness in observation of point sources is important not only for complementing the information from area flux mappers but also for leak detection and repair (LDAR) programs where regularly surveying point sources in a region can enable prompt action to fix malfunctioning equipment (Kemp et al., 2016; Fox et al., 2021). Current LDAR programs rely on a combination of ground surveys, drones, and aircraft, but we will see that satellites have an important role to play.

Let C∈[0,1] denote the observing system completeness for point sources as the fraction of total point source emissions larger than 10 kg h-1 within a domain and time window that can be detected by a given instrument (or constellation of instruments). C is limited by a combination of the instrument detection threshold (CD), spatial coverage (CS), and temporal sampling (CT): 8C=CD×CS×CT. Here CD is the fraction of point source emissions that can be detected on the basis of the instrument's detection threshold, as inferred for example from Fig. 7. CS is the fraction of the domain that the instrument observes at least once within the time window. If there is full spatial coverage within the time window, CS=1.CT=1-1-FpN is the probability for an observed source to be actually detected within the time window given the number N≥1 of observations in the window, the source persistence p (fraction of time that the source is emitting above the detection threshold), and the fraction F of successful retrievals, taken here as the fraction of clear-sky observations. For example, an intermittent source with p=0.2 that is observed with a 1-week return time and 30 % clear skies would have CT=0.96 for 1 year of observations but CT=0.23 for 1 month. If spatial coverage and observing frequency are sufficient, C is limited by the instrument's detection threshold (CD). If they are not (and depending on source persistence and cloud cover), CS and CT may limit observation system completeness rather than CD.

Figure 8 shows the frequency distribution of persistence (p) for 2500 oil and gas point sources detected and quantified by the airborne AVIRIS-NG and Global Airborne Observatory instruments in US field campaigns (Cusworth et al., 2022). The left panel shows the frequency distribution of mean emissions from individual point sources for each persistence bin. From there we can estimate the observing system completeness for any instrument on the basis of its detection threshold, spatial coverage, and return time. The right panel plots the resulting cumulative observing system completeness for the ensemble of 2500 point sources as achieved by either (1) an airborne instrument with 10 kg h-1 detection threshold and bi-monthly (60 d) sampling interval or (2) a satellite instrument with 100 kg h-1 detection threshold and bi-weekly (14 d) sampling interval. The calculation is done for a 1-year time window with 30 % clear skies, assuming CS=0.95 in both cases, and the cumulative results are shown across the range of persistence bins. We see in this example that the two observing systems have comparable success for persistent sources (p>0.5) by trading CD for CT, but the satellite system is better for intermittent sources (p<0.5), despite its higher detection threshold, because of the greater benefit from frequent observations.

Figure 9 further illustrates the trade space between detection threshold and return time for determining observing system completeness. Results are for the ensemble of 2500 point sources with statistics given in Fig. 8. We see from Fig. 9 that an observing system completeness of 0.6 can be achieved by an instrument with a detection threshold of 300 kg h-1 sampling weekly. Such an instrument performs as well as one with low detection threshold but sampling only every 2 months. Achieving an observing system completeness higher than 0.8 requires an instrument with detection threshold better than 150 kg h-1 that samples at least biweekly.

Our calculation of CT as presented above assumes that a point source follows a binary emission frequency distribution (on/off) with constant emissions when on. Actual sources have more complex variability (Allen et al., 2022; Zimmerle et al., 2022). Similar to the analysis of Sect. 5.1, a simple analysis can be done by assuming Gaussian statistics following Hill and Nassar (2019) to estimate the number N of observations needed to quantify a mean point source emission rate (1±δ)Q with relative precision of δ defined by the 95 % relative confidence interval: 9N=1Fp(1.96σδ)2,10σ=σI2+σS2. Here σ is the standard deviation of individual measurements determined by instrument precision (σI) and variability in the source (σS). Using statistics from airborne surveys in the Permian Basin, we find that 71 observations per year (roughly 5 d return time, assuming 30 % clear skies) would be required to estimate annual point source emissions from that highly intermittent population within 50 % (p=0.24, σI=36 %, σS=45 %; Cusworth et al., 2021b). Increasing the required annual emission precision to 35 % would require 145 observations per year (2 d return time). For a less intermittent population (p=0.5), we find N=43 (8 d return time) to achieve 50 % precision and N=87 (4 d return time) to achieve 35 % precision. These observing frequencies can be achieved with a satellite constellation but would be challenging for an airborne program.

The tails of the pdfs for point source emissions are a particular challenge to sample representatively. The pdfs are generally heavy-tailed, resulting in a low estimate of mean emissions (Zimmerle et al., 2022), which may be addressed with very dense sampling (Y. Chen et al., 2022) or with supporting observations from area flux mappers. Persistence is defined in the observations by the frequency of occurrence of emissions above the detection threshold, but non-detection could represent the low tail of the pdf rather than an on/off switch. The definition of persistence may thus depend on the detection threshold, increasing the importance of that threshold as a measure of observing system completeness. Further complicating matters is that the instrument detection threshold is variable, depending notably on the wind speed at the time of observation. This calls for better characterization of the full pdf of emissions from point sources as a means to extrapolate the observations (Allen et al., 2022).