Relating Multi-Scale Plume Detection and Area Estimates of Methane Emissions: A Theoretical and Empirical Analysis

Abstract

Surface emissions of atmospheric trace gases like methane are typically inferred through two methodologies: plume detection and area-scale estimation. Integrating these methods can enhance emission monitoring but remains challenging due to irregular sampling, variable detection sensitivities, and differing spatial resolutions among plume-detecting instruments. In this study, we develop a theoretical framework to link plume-scale and area-scale emission estimates for regions with dense point-source emissions. Our analysis demonstrates that the spatial resolution of plume-detecting instruments influences the observed distribution of plume emission rates. Empirical tests using oil and gas emissions data from the Permian Basin reveal a robust linear relationship between summed gridded plume emission rates and area-scale estimates. After accounting for variability in sampling of the plume detectors, area-scale estimates derived from TROPOMI flux inversions strongly correlate with weekly plume sums (R² > 0.94, P < 0.005). We also assess the feasibility of using plume data to inform area-scale estimates within a Bayesian assimilation framework and find that plume assimilation improves the constant EDF inventory, bringing it into agreement with independent TROPOMI-derived emission estimates. This work highlights that, given sufficient sampling and favorable observational conditions, plume observations from aircraft, satellites, and in situ instruments can inform and enhance area-scale methane emission estimates, particularly within the oil and gas sector.

Short abstract

We present a method to use plume observations from aircraft and satellites to inform and enhance area-scale methane emission estimates in oil and gas sector.

1. Introduction

Understanding methane emissions is crucial for developing climate change mitigation strategies and accurately predicting future climate. New observational techniques for detecting methane plumes from point sources have advanced our understanding of methane emissions.¹⁻¹² Reducing methane emissions—especially from large point sources (often called superemitters)—is now central to climate change mitigation efforts.¹³⁻¹⁵ Plumes are detected over a wide range of spatial scales (typically 1 m–10 km) but are limited to temporal snapshots (<1 h) of the emissions from a single point source or a cluster of point sources. An area-scale observing system provides area-averaged estimates of emissions by aggregating emissions at spatial (>10 km) and temporal (>weekly) grid cells. Area estimates trade spatial resolution for improved accuracy in quantifying the total magnitude of emissions. In this paper, we present a theoretical framework that relates the sum of plume detections to area emission estimates over a region of dense point source emissions.

Area estimates of emissions are derived from bottom-up approaches^16,17 and top-down flux inversions.¹⁸⁻²⁴ Bottom-up inventories typically quantify emissions by combining emission factors (e.g., emission per wellhead) with activity data (e.g., number of wellheads). However, emission factors vary across operating conditions, leading to inaccuracies in the emission estimates. Top-down approaches quantify emissions by comparing atmospheric chemical transport model (CTM) simulations to observed atmospheric concentration gradients resulting from those emissions. The diffusive and chaotic nature of atmospheric transport, along with limited observation coverage and the computational cost of CTM simulations, limit the spatial resolution of top-down area estimates.²⁵⁻²⁸

Plume detections use sharp enhancements in a concentration field caused by emissions from a single point source or a cluster of point sources. In situ plume-detecting instruments can be mounted on automobiles, aircraft, or the ground. Column-observing plume instruments are typically deployed onboard aircraft or satellites. These remote sensing instruments can be either active²⁹ or passive (e.g., GHGSat, Sentinel-2, PRISMA, Carbon Mapper, MethaneSAT³⁰⁻³³). Plume detections are used in Leak Detection and Repair (LDAR) techniques, focusing on fixing anomalous methane emitters to mitigate emissions. Observed plumes can account for a large fraction of the emission rate [kg h^–1] in certain sectors, providing an advantage for targeted mitigation efforts.^29,34,35

Several studies have attempted to use plume detection to inform area-scale emission estimates. For instance, some studies have generated regional and national inventories that account for the large point-source emissions missing from traditional bottom-up inventories.^8,36−38 These studies extrapolate plume detections from measured facilities, assuming some degree of temporal persistence in the emissions. They account for emissions below the detection limit of plume instruments by incorporating bottom-up emission factors.³⁶ Other investigations have used plume detections to refine the prior emissions in flux inversion estimates.³⁹

Because area estimation methods quantify the total emissions from one or multiple sectors together, they are directly related to regional total emissions. However, the relationship of plume detections to regional total emissions is complex for several reasons. First, the spatial resolution (or ground pixel size) varies by orders of magnitude among plume-detecting instruments: less than 20 m for hand-held Optical Gas Imaging (OGI) cameras and ground/aerial in situ instruments,^5,6,40−42 1–150 m for aerial imaging instruments,^3,31,34,43 and ≈4–500 m for satellite imaging instruments.^{7,32,33,44−50} The TROPOspheric Monitoring Instrument (TROPOMI), originally designed for providing top-down constraint in flux inversions, also observes methane plumes but at a pixel size of roughly 7 km.^{7,46,47,49,51−53} Second, detection sensitivity varies among plume instruments. For instance, Sentinel-2, a multiband instrument with a 20 m pixel utilizing only spectral bands from the observation day, can detect point sources emitting over 1 t h^–1.³³ GHGSat, with a similar spatial pixel, can detect plumes with emission rates below 100 kg h^–1 under favorable observation conditions.^29,54,55 Third, plumes only observe a fraction of the total emission rate [kg h^–1] in a region. This emission rate fraction can be quite large depending on the instrument and sector. However, the detected mass enhancement in plumes represents only a tiny fraction of the total emitted mass [kg]. For instance, an aircraft campaign might sample the emissions field of a region for tens of hours over a year, observing only a very small mass fraction of the monthly or annual emissions. Plumes may represent a significant mass fraction of emissions if they originate from persistent sources, although this assumption is not always valid.^10,56 Fourth, intermittent point source emissions can bias temporal mean estimates of emissions. Both in situ and passive total column imaging instruments tend to observe methane concentrations in the late morning or afternoon to detect point source or facility emissions. In situ instruments prefer a well-developed planetary boundary layer, and passive imaging instruments prefer strong solar backscatter light. The emission effects of daytime maintenance operations in the oil and gas sector can be particularly pronounced.^56,57 As a result, emission estimates based exclusively on afternoon measurements may not accurately represent the true temporal mean.

In the next section, we present our theoretical framework to relate the sum of plume detections and area estimates in dense point source emission fields. We derive a statistical relation between plume sums and area estimates, taking into account instrument detection sensitivity, sampling, and the periodicity of emissions. In Section 3.1, we describe the oil and gas emission data sets from the Permian Basin used in this study. In Section 4, we test the statistical relationship between plume sums and area estimates using the Permian Basin data. In Section 5, we present approaches to evaluate and refine area emission estimates using plume observations. Finally, we discuss our findings in Section 6.

2. Theory

2.1. Definitions

Here we define and distinguish point sources, plume detection, and area-scale emission estimates.

• Point source: a source of emission with a small spatial extent, less than a few meters, smaller than the spatial pixel size of typical plume-observing instruments. The emission rate of a point source has the unit kg h^–1.

• Plume detection: the detection of emissions from a single point source or a cluster of point sources, observed as a group of concentration-enhanced pixels by an imaging instrument. In situ instruments also detect plumes as a sharp enhancement in concentrations downwind of one or more point sources. The emission rate of a plume has the unit kg h^–1.

• Area-scale estimate: estimates of total emissions over a large spatial (>10 km) and temporal (>week) interval for a sector or sum of sectors. Area estimates are derived using top-down flux inversions or bottom-up approaches. An area estimate of emissions has the unit kg h^–1 m^–2.

Emissions from point sources in a dense emission field, such as an oil and gas basin, can be observed both as area estimates and plume detections, but these observations have different spatial specificity, and they measure different proportions of total emissions. Plume detections and point sources are sometimes used interchangeably in the literature, assuming a plume originates from a single point source. For our analysis, we emphasize the distinction between a point source and a plume detection because a plume can contain emissions from multiple point sources.^39,49

A single plume detection entry in a data set typically includes at least three values: (1) the plume’s source location (latitude and longitude), (2) the time of detection, and (3) the emission rate with uncertainty estimates. Some plume data sets also provide wind speed data used for emission rate quantification, as wind is generally considered the main source of error in these calculations.⁵⁸ Area estimate data sets are typically provided in a gridded format, with each grid cell representing the mean emission rate over specified spatial and temporal intervals. Some, but not all, area-scale estimates include uncertainty metrics or even a complete error covariance matrix.^59,60 Flux inversions do not always provide the full posterior error covariance because computing it becomes computationally expensive or even impractical when optimizing large state vectors in top-down approaches—often implemented using variational inversion methods.^22,61 The emission values of an area estimate may represent total emissions from a grid cell (typically from top-down inversions) or sector-specific emissions (typically from bottom-up inventories like EDGAR and EPA).^16,62 Top-down flux inversions sometimes offer sectoral partitioning but still rely heavily on bottom-up information for sectoral attribution.²⁴

2.2. Conceptual Illustrations

Here, we conceptualize how the spatial pixel size of plume detectors can affect the number of possible plume detections and their emission rates when observing a dense point source emission field.

2.2.1. Impact of Instrument Pixel Size on Plume Detection

Consider an observing system monitoring a dense point source emission field within a grid cell c of size l_c × l_c [m²]. The observing system uses a concentration imaging instrument i with a spatial pixel of size l_i × l_i [m²]. Let us assume that the spatial resolution is the same as the spatial pixel size for this hypothetical instrument. Then, the observed concentration field is a discrete representation of the underlying emission field, with the spatial resolution determined by the instrument pixel size. Suppose the imaging instrument detects a plume by identifying a group of enhanced pixels forming a Gaussian plume shape. An enhanced pixel can be roughly defined as one where the concentration value exceeds the background by at least 2 σ_i, where σ_i is the instrument’s pixel concentration uncertainty. Let denote the area required to confidently detect a Gaussian-shaped plume. We define the square root of this area, δ_i [m], as the emission spatial specificity. δ_i quantifies the instrument’s ability to differentiate emissions from distinct point sources.

To keep our conceptual exercises (Figures 1 and 2) straightforward, we assume δ_i varies linearly with l_i for instruments sharing a similar concentration precision. In other words, we treat the number of pixels needed to detect a plume as roughly constant across different spatial scales. In the real world, δ_i also depends on the instrument’s signal-to-noise ratio (SNR), wind speed, surface albedo, and the distribution of point sources, making precise estimates for a specific instrument difficult. Our primary aim here is not to determine the exact value of δ_i, but rather to demonstrate its effect on plume detection. These exercises also ignore spatially varying systematic measurement errors that could influence plume detections.

Figure 1.

Conceptual illustration of the influence of instrument pixel size l_i and precision error σ_i on plume detection. Panel (A) shows the column-averaged concentration field from a CTM simulation, featuring plumes from ten point sources. Each panel represents a coarser (left to right) and/or noisier (top to bottom) version of the same concentration field (Panel A) over the same spatial domain. To simulate pixel precision error, Gaussian random noise with a standard deviation of σ_i is added to the panels in the leftmost column. The precision error reduces from left to right panels with aggregation across adjacent pixels. N represents the number of distinct plumes identified in each panel. The grid cell size (l_c) and instrument pixel size (l_i) are marked in Panel (L). A rough estimate of emission spatial specificity, δ_i, is given by the area of black ellipses marked in the second row. Note that the units are kept arbitrary, illustrating the adaptability of the diagram to a wide range of spatial scales and trace gas plumes. Although the original WRF-Chem CTM run was performed at 1 × 1 km² spatial resolution, this conceptual illustration can be extended to a wide range of spatial resolutions (1 m–10 km). Our determination of N is subjective, akin to real-world scenarios where a human flags a successful plume detection.

Figure 2.

Conceptual illustration of the impact of pixel size on plume emission rate distribution in a hypothetical dense point source emission field. Panel (A) presents the POD curves for two hypothetical instruments, Y (green) and Z (red), each with a pixel size l_i = 1 unit. Panel (B) shows the expected changes in POD when aggregating instrument pixels to l_i = 2 units. Panel (C) displays the frequency distribution of plume emission rates for l_i = 1 unit, showing the true distribution in black and observed distributions for instruments Y and Z. Panel (D) shows the frequency distributions for l_i = 2 units. Panels (E) and (F) show the cumulative distributions and fraction of total emissions observed by the two instruments at the two l_i values.

Figure 1 displays a snapshot of the column-averaged concentration field of a trace gas from a Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) CTM simulation at 1 × 1 km² spatial resolution with ten point emission sources. Using this figure, we conceptually examine two physical effects on the number of plume detections (N): (1) reduction of N due to clustering of plumes from distinct point sources as l_i increases, and (2) reduction of N as pixel precision error increases.

Figure 1 illustrates that as l_i increases (from left to right panels), plumes from individual point sources cluster into larger plumes, reducing N. This clustering causes the loss of information about the origins of individual plumes from specific point sources, leading to a degradation of the emission spatial specificity δ_i. If the spatial distribution of the point sources is dense and uniform enough, the number of point sources will be proportional to the area, and δ_i degrades proportionally with l_i. The fewer cluster plumes formed by the merging of smaller plumes will have higher emission rates. This emission rate boosting also occurs when a plume from a large source masks smaller point sources within its area, as emissions from the smaller sources enhance the concentration of the large plume. Consequently, we expect differences in plume emission rates observed by instruments with varying pixel sizes: AVIRIS-NG (l_i = 5 m), GHGSat (l_i = 25 m), Carbon Mapper Tanager-1 (l_i = 30 m), MethaneSAT (l_i > 100 m), and TROPOMI (l_i > 5 km). At very coarse spatial resolutions (l_i = 20 unit), individual plumes and their sources cannot be identified. In such cases, area emission estimation methods—like atmospheric flux inversions and mass balance techniques—are used to quantify emissions.^39,63−66

As the precision error σ_i increases (from top to bottom panels in Figure 1), the number of plume detections N decreases. Interestingly, with high precision error, it is possible to detect more plumes at coarser spatial resolution than at finer resolution. For instance, in the bottom row of the figure (σ_i = 20 units), more plumes are detected at spatial scales of l_i = 3 and 6 units than at l_i = 1 unit. This effect is observed in real-world scenarios. For example, TROPOMI can detect plumes from large areas like cities, but when zooming in with fine spatial resolution instruments, a fine-scale plume may not be observed, likely because instrument precision error dominates the plume signal at these finer spatial scales.⁵³

2.2.2. Impact of the Instrument Pixel Size on Emission Rate Distribution of Plumes

A plume instrument’s Probability of Detection (POD) function represents the likelihood of detecting a single point source plume at a specific emission rate. The POD curve typically has a sigmoid shape (see Figure 2A): the POD approaches 0 for small point emissions or diffused area sources that create weak plumes (where the concentration enhancement within a pixel is below the instrument’s detection capability) and approaches 1 for large point source emission rates. Observation conditions influence the POD.^54,55 Factors such as surface albedo, solar zenith angle, wind speed, and the detector’s altitude all contribute to this effect. For instance, variations in surface albedo and solar zenith angle alter the instrument’s signal-to-noise ratio (SNR), which in turn impacts measurement precision and modifies the POD curve. Additionally, higher wind speeds can dilute the concentration enhancement captured per pixel, making plume detection more challenging.

Figure 2 illustrates how the instrument pixel size affects the emission rate distribution of plume detections in a dense point source field. It highlights how precision error and spatial resolution jointly influence observed plume emission rate distributions. For this conceptual exercise, we assume a spatially uniform distribution of point sources, with their emission rates following a Gamma distribution (parameters: shape = 0.75, scale = 80), and that the POD of hypothetical instruments follows logistic functions. Our inferences should remain valid for other similarly shaped choices of emission rate distributions and POD functions.

Figure 2A compares the POD functions for two hypothetical instruments. P₅₀ [kg h^–1] of an instrument denotes the emission rate at which the POD value is 50%, meaning half of the plumes at this emission rate will be detected by the instrument. At l_i = 1 unit, the P₅₀ of instrument Y is 25 kg h^–1, which is four times better than that of instrument Z at 100 kg h^–1. This difference may result from instrument Z having four times higher pixel precision error σ_i than instrument Y. The middle row panels of Figure 2 show the frequency distribution of true emission rates (black) from the l_i × l_i pixels and the corresponding emission rate distribution for the two instruments’ plume detections, which is given by the POD curve multiplied by the emission rate distribution. Four pixels are aggregated together in the right columns of the figure. As per the assumption of our conceptual exercise, some notable effects occur:

• 1.
  The P₅₀ of the instruments worsens by roughly a factor of 2 due to the combination of two effects:

  • Aggregating pixels dilutes the plume enhancement signal of a point source by roughly a factor of 4.
  • Averaging the instrument pixel precision error over four pixels reduces the precision error σ_i by roughly a factor of .

  The net effect, given by the ratio of these two factors, causes the P₅₀ to worsen by about a factor of 2.

• 2.The emission signal improves by a factor of 4. A 2 × 2 pixel group contains four times the point sources compared to a 1 × 1 pixel, thus increasing the amount of emitted mass per unit time under a pixel.

As the spatial pixel size l_i increases, pixels with low total emissions become fewer, altering the emission rate distribution. According to the central limit theorem, when identically and independently distributed (IID) pixel-wise emissions are summed, the distribution becomes more bell-shaped, with the randomness of individual emissions averaging out, leading to a more symmetric, Gaussian-shaped emission rate distribution. Additionally, the expected value of the per-pixel emission rate shifts to the right by a factor proportional to . Note that the peak of the frequency distribution shifts by the clustering amount only if the distribution is Gaussian (mode = mean); for skewed distributions, the shifts differ.

The bottom panels of Figure 2 display the ‘true’ and observed cumulative emission distributions, which are normalized relative to the true emission distribution. These cumulative distributions illustrate the fraction of total emissions represented by plumes detected at or above a given emission rate. For instance, Instrument Y detects nearly 100% of the total point source emissions at l_i = 2 but only 60% at l_i = 1. This highlights the trade-off between spatial specificity and the ability to accurately estimate total emissions at different pixel sizes l_i.

The conceptual exercises in Figures 1 and 2 introduce the concept of clustering and illustrate the trade-offs between detection sensitivity and spatial resolution in instruments. It is important to note that the exact magnitudes of plume clustering effects and the dependence of instrument precision noise on pixel size will deviate from the values presented in these conceptual exercises, as they are influenced by factors such as the spatial distribution of point sources, pixel sizes, error correlations, and the instrument’s design and detection capabilities. Generally, fine spatial resolution instruments observe a lower fraction of total emissions but provide good emission spatial specificity, offering better information on the location of point sources. Conversely, instruments with coarser spatial resolution detect a higher fraction of total emissions but offer reduced spatial specificity. The conceptual illustration allows for generalization to include detections by instruments ranging from meter-scale (typically capturing a single point source) to kilometer-scale resolution (typically capturing emissions from a cluster of point sources). In some sense, an area emission observing system is an extreme case of a coarse-spatial-resolution instrument designed to be sensitive to 100% of the total emissions over a large area but lacking point source location information.

2.3. Statistical Relationship between Area Estimates and Plume Sums

We present a statistical relationship between area estimates of grid cell emissions—which represent mean emissions over specific spatial and temporal intervals—and the sum of plume emission rates within each grid cell. The complete derivation of the relationship is given in Supporting Information (SI) Section 1. Several factors must be considered when relating area estimates to plume sums. First, instruments with different pixel sizes (see Figure 1) or detection sensitivities must be treated separately in this relationship. Second, the extent of sampling of the emission field by the plume instrument must be considered, as it determines the number of plume detections and, consequently, the magnitude of plume sums. Third, potential temporal biases in the sampling of the emission field must also be accounted for.

Consider an emission sector or subsector category (sector’s component), s, within a large grid cell c of area l_c × l_c [m²] composed of densely distributed point sources. The area l_c × l_c can roughly range from 25 × 25 km² (a regional flux inversion grid cell) to more than 5° × 5° latitude–longitude (a global flux inversion grid cell). The time interval associated with c can be between a week and a year, corresponding to typical flux inversion periods.

Suppose a plume-detecting instrument i scans different portions of c during a number of scans within the time interval of c. From these scans, plume detections are identified and quantified. Let η_ic [unitless] represent the sampling of the emission field within grid cell c by instrument i during its time interval. η_ic is given by the sum of the ratios of the total of the ground areas covered by each of the scans to the grid cell area .

Let y_ics [mass time^–1] denote the sum of emission rates of the plume detections by i in the spatial and temporal extents of c. Let x_cs [mass time^–1 ] represent the total emission rate from c of all emissions of sector s. The relationship between the plume emission sums y_ics and the total area estimates x_cs is given by

1

Here, κ_is [unitless] is periodicity bias correction for the temporal sampling bias of instrument i due to periodic (continuous or intermittent) emissions from sector s, (see SI Section 1). The variable τ_ics ∈ [0, 1] represents the plume factor, which is the fraction of the total emissions from sector s that are expected to be observable by instrument i during one complete scan of grid cell c, assuming no periodicity bias: , when η_ic = 1 and κ_is = 1. τ is a function of the instrument’s plume detection sensitivity or the POD under the observing conditions of c. Note that, in our model, y_ics can be greater than x_cs depending on the amount of sampling of the emission field of c. For instance, consider a hypothetical instrument for which τ_icsκ_is = 1. In this case, y_ics = x_cs for a single complete scan of the grid cell (η_ic = 1), but if the grid cell is completely sampled 20 times by the instrument during the interval of c, then y_ics = 20x_cs.

3. Materials and Methods

We briefly describe the data sets and the data processing methods used in the empirical tests (Section 4) and the applications (Section 5) of plume data sets. The Bayesian inversion method and the data sets are described in detail in the SI Sections 2 and 3, respectively.

3.1. Data

We use plume detections and area estimates of oil and gas emissions in the Permian Basin, USA. We use plume data collected by two airborne imaging instruments (referred to as the “ANG” and “GAO” instruments from here on) during the Carbon Mapper campaign in the fall of 2019.⁵² The Integrated Mass Enhancement method (IME) was used for the emission quantification of these plumes.³¹ The plume data cover a six-week period from September 24 to November 4, 2019. We use the gridded area estimates from two sources: (1) concurrent weekly top-down TROPOMI flux inversions⁹ and (2) the annual mean Environmental Defense Fund’s (EDF) 2018 bottom-up inventory,⁶⁷ both at a spatial resolution of 0.25° × 0.3125° latitude and longitude (≈25 × 25 km²).

Following the analysis presented in Sections 2.2.1 and 2.2.2, ANG and GAO are treated as different plume detectors due to differences in their observation configurations during the 2019 Carbon Mapper campaign. Their pixel sizes and precision errors differed because the instruments were flown at different flight altitudes. Additionally, their plume detection capabilities were further distinguished as GAO was equipped with a high-resolution visual camera to assist in detecting plumes.

Figure 3 shows the gridded area emission estimates and the weekly coverage (shown as η) from the two aircraft instruments. Sampling occurred over multiple flight tracks each week. For each flight track j_i, we calculate the fraction of c covered, denoted by I(j_i, c). We then compute η_icw by summing these grid cell fractions of flight tracks during the week w:

2

The η_icw values are shown in Figure 3. Table 1 presents weekly values of the number of plume detections and sampling across the Permian.

Figure 3.

Emissions data set used in this study. The top row shows the gridded area estimates for the Permian Basin oil and gas emissions from (A) TROPOMI (top-down) flux inversion and (B) EDF (bottom-up) inventory, both at a spatial resolution of 0.25° × 0.3125° latitude-longitude. The EDF inventory was prepared for the year 2018, while the TROPOMI estimates shown here are the six-week (September 24 to November 4, 2019) mean of the flux inversion posterior from Varon et al.⁹ The thick black contour marks the geological extent of the Permian Basin, highlighting two major emissions hotspots corresponding to the Delaware (West) and Midland (East) basins. The middle and bottom rows show the weekly sampling (η_icw) of plume detectors during the Fall 2019 Carbon Mapper survey in the Permian Basin. The sampling factor for the ANG and GAO instruments is provided for the weekly grid cells of 0.25° × 0.3125° latitude-longitude. η_icw can exceed 1 when a grid cell is observed more than once a week. Black dots indicate cells with η_icw < 0.1. See also Table 1.

Table 1. Weekly Statistics of the Plume Detections by the ANG and GAO Instruments during the Carbon Mapper Fall 2019 Permian Survey^a.

	GAO instrument			ANG instrument
week	# plumes	τiswκisw	∑c∈Permian,wηicw	# plumes	τiswκisw	∑c∈Permian,wηicw
Sep-27				266	0.68	38.7
Oct-04				318	0.87	22.9
Oct-11	198	1.01	16.9	351	0.7	38.7
Oct-18	187	1.0	20.6	709	0.81	48.6
Oct-25	396	1.05	23.8	310	0.67	29.1
Nov-01	212	0.89	16.7
mean	250	0.99 ± 0.06	19.5	402	0.75 ± 0.08	37.2

^a# plumes is the number of plume detections in week w. ∑_{c∈Permian,w}η_icw is the weekly grid-cell sampling sums (see Figure 3) of the instruments. τ_iswκ_isw is the plume factor times periodicity bias estimated by taking the ratio between plume sums and area emissions. τ_iswκ_isw values are used in the plume inversions (Section 5.2) and discussed further in Section 6 (see eq 3). ± denotes 1-standard deviation spread.

3.2. Plume Inversion Setup

Current atmospheric flux inversion methods utilize satellite or in situ concentration observations in conjunction with a CTM to inform grid-scale area estimates. Plume detections can provide independent emission observations that can enhance these area estimates. In Section 5.2 we perform Bayesian assimilation of gridded plume sums (referred to as “plume inversion”) on grid cell area estimates using the plume sum model (eq 1). We provide a brief summary of the methodology here (detailed description of the method is given in SI Section 2.). The plume inversions optimize a state vector representing weekly area estimates between September 24 and November 4, 2019, on a 25 × 25 km² grid within the Permian Basin, focusing on the oil and gas sector. Each week, 235 state vector elements are optimized. We refer to the plume inversions as Plume-EDF inversion and Plume-TRO inversion, which respectively use EDF and TROPOMI emission estimates as priors.

As per eq 1, the product of the plume factor and periodicity bias (τ_icsκ_ics), along with the temporal sampling factor (η), is required to link area-based emission estimates with plume sums. The true values of τ_icsκ_ics for the ANG and GAO instruments observing Permian oil and gas sector emissions are currently unknown. To obtain these, we aggregate TROPOMI and plume observations across space and time. First, we compute weekly τ_iswκ_isw by comparing each instrument’s plume detections with TROPOMI-based emission estimates. Specifically, for instrument i and sector s, we use:

3

where both the plume detections and TROPOMI-based quantities for a grid cells c are summed over the Permian region for the week w. We then average these weekly values to estimate a single best-estimate τ_isκ_is for each instrument, which is applied uniformly over the six week period in the inversions. Table 1 presents the weekly plume counts, the corresponding τ_iswκ_isw values, and the η_ic values.

4. Empirical Analysis

4.1. Probability Density Functions (PDFs) of Plumes

Figure 4 shows the PDFs of weekly plume detections from the ANG and GAO instruments. The two instruments exhibit different emission rate PDFs; GAO shows superior plume detection capabilities, identifying more plumes below 30 kg h^–1. The expected values of the weekly PDFs for the ANG plume detections range from 318–485 kg h^–1 (mean = 417 kg h^–1), while for GAO detections, they range from 243–443 kg h^–1 (mean = 333 kg h^–1). This difference is expected because GAO has better detection sensitivity. GAO operated at an altitude of 4.5 km, resulting in less atmospheric interference and a finer surface pixel size (GAO l_i = 4.5 m) compared to ANG, which operated at 8 km altitude (ANG l_i = 8 m). Moreover, GAO augmented its plume observations with high-resolution visual imagery to enhance detection accuracy and minimize surface artifacts (see SI Section 3).

Figure 4.

Probability density functions (PDFs) of methane plume detections by ANG and GAO aircraft instruments during the Fall 2019 Carbon Mapper survey in the Permian Basin. The top panels display the weekly emission rate PDFs. The bottom panels show the corresponding weekly plume wind speed PDFs. Each line color corresponds to a different week, as indicated in the legends. The emission rates and wind speeds are binned in logarithmic intervals. The expected values of the weekly distributions are given in the legends’ parentheses and are marked with the colored vertical lines at the bottom of each panel.

The standard deviation (SD) of the expected values of the weekly PDFs for ANG is 13% (relative to the multiweek mean). For GAO, the corresponding SD is larger at 28%. The ANG instrument’s survey was strategically designed to repeatedly observe regions with high emissions (see Figure 3), whereas the GAO survey aimed to cover the entire Permian Basin at least once. Therefore, GAO encountered a wider range of observation conditions than ANG, resulting in greater variability in its POD and the expected values of plume emission rates across the weeks.

Figure 4 also displays the 10 m wind speed data from the High-Resolution Rapid Refresh (HRRR) model, which was used for emission rate quantification of the plumes by Cusworth et al.⁵² Since POD is sensitive to wind speeds,⁵⁵ the variation in GAO’s observational conditions is reflected in the weekly wind speed distributions, where the standard deviation of GAO’s weekly wind speed expected values is 45%, compared to only 20% for ANG (relative to the multiweek mean wind speeds). The larger variation in GAO’s wind speeds results in greater variability in its POD and, consequently, in more diverse plume PDFs. For GAO, there is a noticeable difference between emission rate and wind PDFs between two pairs of weeks: the weeks of Oct-11 and Oct-18 differ from Oct-25 and Nov-01. The R² between the weekly expected values of the log of wind speed and the log of emission rates is 0.98 for GAO and 0.44 for ANG, suggesting a strong influence of winds on the emission rate PDFs.

Despite the plume detections occurring at different observation locations within the Permian Basin (Figure 3), the shapes of the distributions for GAO and ANG are quite similar across the weeks, with major differences explained by wind speed variations and other spatial factors affecting the POD. After accounting for these variations, we infer that the PDF of the point source emission rates in the Permian Basin remains strongly correlated over time.

4.2. Comparison of Plume Emission Rate Sums with Area Estimates

We evaluate the relationship between total plume emission rates and area-based emission estimates in the Permian Basin. Figure 5 shows the weekly time series of plume sums and area estimates derived from the top-down TROPOMI inversion and the bottom-up 2018 EDF inventory. Each area estimate is adjusted for aircraft sampling using η. The 2018 EDF inventory provides only spatial emission patterns for the Permian Basin, and these patterns remain constant each week because the inventory does not include data specific to the 6 weeks in 2019. However, the temporal variability of the sampling factor introduces variability in the sampling-adjusted area estimates, as shown in the figure. In the case of TROPOMI flux inversion, the temporal variability in the time series arises from both sampling and actual emission variability.

Figure 5.

Comparison of time series of weekly plume emission sums (=∑_{c∈Permian,w}y_ics) and area emission estimates. The top-down area estimates (concurrent weekly TROPOMI flux inversion) are shown in red, and bottom-up area estimates (annual 2018 EDF inventory) are shown in blue. The area estimates are adjusted for instruments’ sampling (=∑_c∈Permianη_icx_cs). The R² between area estimates and plume sums are given in the respective colors. The dashed horizontal lines mark the means of the time series.

GAO and ANG show correlations of (R² = 0.84, P = 0.09) and (R² = 0.59, P = 0.13), respectively, when comparing plume sums to the temporally constant EDF inventory estimates. This indicates that much of the variability in weekly plume sums is due to the variability in weekly sampling of the plume instruments. Using TROPOMI’s top-down area estimates results in stronger correlations: GAO (R² = 1.0, P = 0.001) and ANG (R² = 0.95, P = 0.005). These high correlation values demonstrate that eq 1 effectively relates area estimates to plume sums across large spatial domains such as the Permian Basin. The higher correlation for TROPOMI inversion area estimates in comparison to the constant EDF inventory also shows that the TROPOMI inversion captures the temporal variability of emissions.

Figure 6A presents the R² values between area estimates, plume counts, and plume emission rate means and sums. The mean of plumes correlates negligibly with area estimates (R² ≤ 0.26 for both EDF and TROPOMI). For GAO, R² goes up to 0.26, but it remains highly uncertain (P = 0.51). The strong area estimates’ correlation with plume sums but negligible correlation with plume means implies that there should be a good correlation between the plume counts and area estimates. For these, we find an R² range of 0.31–0.78.

Figure 6.

Correlation (R²) between properties of weekly plume detections and sampling-adjusted area estimates. Panel (A) shows the correlation for the weekly aggregates over the Permian (∑_c∈Permianη_icx_cs vs ∑c_∈Permiany_ics). Panel (B) shows the correlation at the grid cell level (η_icx_cs vs y_ics). The plot compares the plume emission rate means, sums, and the number of plumes (count) with top-down (TROPOMI, light-blue shaded regions) and bottom-up (EDF) area estimates. Green bars represent ANG data, while gray bars represent GAO data. R² values of <0.02 are marked with “*”.

Figure 6B presents the R² values at the grid cell level (η_icx_cs vs y_ics). As expected, R² diminishes at smaller spatial scales due to increased noise. For plume means, R² is negligible for both bottom-up and top-down estimates. The plume sum R² values with the bottom-up EDF inventory are 0.63 and 0.44 for ANG and GAO, respectively, surpassing those with the top-down TROPOMI, where the respective R² values are 0.58 and 0.32 (P < 10^–15 for all grid-scale plume sum R²). ANG shows a stronger correlation with area emissions at the grid scale, likely because it samples the emissions field more extensively by repeatedly observing high-emission areas under more consistent conditions than GAO. As a result, individual ANG data points have lower relative noise. In contrast, GAO includes pixels with very low emission activity where noise can dominate because it samples areas away from major emission sources in the Permian basin.

The poor correlation between plume means and area emissions can be explained as follows: the plume PDFs are independent of emission activity factors. Therefore, while area emissions, plume sums, and plume counts scale with activity factors, plume means do not (see SI Section 1). When wind speed variability is introduced, it adds additional variability to all three plume quantities. For plume sums and plume counts, wind speed variations introduce noise, potentially reducing the correlation with area estimates from the ideal value of 1. In the case of plume means, starting from an expected correlation of zero under ideal conditions, wind speed variability could theoretically introduce random fluctuations that might increase the observed correlation with area estimates slightly over a few data points (Figure 6A). However, wind speed fluctuations across large sample sizes are expected to be uncorrelated with area emissions or activity factors, therefore the correlations between observed means and area estimates are near zero at grid cells (Figure 6B).

In our analysis, we presented results at two spatial scales: basin total and grid cells. While the correlation is lower at the grid cell level compared to the basin total due to increased noise, it still remains strong (for instance, R² of roughly 0.6 for ANG plume sum versus both EDF and TROPOMI). These good correlation values indicate that plume sums align well with area estimates even at the grid scale. The correlation is expected to improve even further when grid cells are aggregated.

The errors in plume sums, EDF inventory, and TROPOMI estimates are expected to be independent when representing true emissions. In the quasi-Kalman-filter approach of Varon et al.,⁹ the posterior estimates are nearly independent of the EDF inventory prior, which is used only for the first week of the multiyear inversion. Assuming some level of independence of errors of these three estimates, if any two of them agree while the third does not, it suggests that the first two are closer to the truth. A poorer correlation of plume sums with TROPOMI flux inversions at the grid cell level suggests that the EDF bottom-up inventory and plume data likely have superior spatial information at fine scales. This also indicates that TROPOMI is less effective at high spatial resolutions for constraining emissions, likely due to limitations in the CTM and TROPOMI coverage and resolution. In contrast, the better agreement of weekly totals between TROPOMI and plume data shows that the TROPOMI inversion’s total weekly emission estimates for the Permian are better than those from the constant EDF inventory.

4.3. Correlation of Plume PDFs

Our empirical analysis shows that the mean of plume emission rates does not correlate with area estimates for a sector across space and time. However, the sums of emission rates—and, to a lesser extent, the number of plume detections—exhibit a strong correlation with area estimates. These empirical observations can be explained by assuming that the true PDFs of point source emission rates within a sector are highly correlated in space and time, remaining nearly invariant over regional and temporal intervals, such as the Permian Basin emissions over several weeks. In Figure 4, we showed that variations in the observed plume PDFs—and their expected values—are predominantly driven by changes in the instrument’s POD, due to factors such as fluctuations in wind speeds.

The spatial and temporal correlation of point source PDFs can be physically explained as follows. The distribution of point source emissions within a sector depends on (1) the proportions of different components (e.g., valves, small pipes, large pipes, wellheads, etc.) and (2) the maintenance and quality of emission-causing components. Both these factors are expected to correlate because they are shaped by technological, economic, and regulatory contexts, which exhibit spatial and temporal correlations. Therefore, the point source PDF for a sector in a given region is determined by the proportions of components and their respective emission PDFs.³⁷ Consequently, point source PDFs for sectors like oil and gas under similar administrative and economic conditions, such as the Permian Basin, are expected to be similar. Plume PDFs are likewise correlated because they represent spatial aggregations of point source emission PDFs at the emission spatial specificity of the plume-detecting instruments (see Section 2.2.2). Emissions in different administrative and economic regions, such as oil and gas operations in Turkmenistan versus the Permian Basin, are expected to exhibit different PDFs. For instance, Turkmenistan has a higher proportion of large emitters exceeding 1000 kg h^–1.⁶⁸

5. Applications

5.1. Evaluating Area Estimates Using Plumes

Evaluating the accuracy of area estimates from flux inversion and bottom-up inventories poses several challenges. The inversions constrain total emissions from various sources across large areas. The area estimates are typically evaluated against atmospheric concentration measurements from in situ and/or TCCON sites, using a CTM to simulate atmospheric concentrations resulting from the emissions. However, errors in the CTM are a major component of the overall flux inversion errors.²⁵⁻²⁷ Consider a scenario where both the assimilation observations and the validation data used in inversions are accurate, but the inversion relies on a CTM that contains errors. These CTM errors will propagate into the emission estimates when the inversion attempts to match the observations by adjusting the emissions. Since the observation and validation data are consistent, the simulated posterior field will agree with the validation data. Therefore, evaluating inversion estimates using CTM simulations may not reveal CTM-related errors.

The previous section showed that plume sums strongly correlate with area estimates. This strong correlation enables the use of plumes to evaluate area estimates. The differences between the correlation of plume sums with temporally variable top-down and constant bottom-up emissions can provide insights into the ability of plume observations to evaluate temporal variations in area emissions. We define a metric ϕ_T called the plume temporal sensitivity to measure this ability.

4

Here, R²_TS is the correlation of plume sums with area estimates that have both temporal and spatial variations, while R²_S is the correlation with area estimates that are constant in time and only have spatial variation. Subtracting the correlation with constant emissions removes the R² dependence on the spatial patterns of emissions and the sampling factor η.

We use the correlation of plume sums with TROPOMI and EDF as R²_TS and R²_S, respectively, to test the capability of the ANG and GAO plumes. The value of ϕ_T is 0.36 for ANG and 0.16 for GAO (the difference between the R² for TROPOMI and EDF in Figure 5). The modest ϕ_T for GAO is likely due to its lower sampling (993 plumes over 4 weeks) of the emission field and greater variations in observation conditions. In contrast, ANG performed repeated observations in the emission-dense regions of the Permian Basin, leading to a detection count of 1954 plumes over 5 weeks, approximately double the number detected by GAO.

An implication of our PDF correlation assertion (Section 4.3) is that plume instruments with detection sensitivities poorer than those of ANG and GAO should also be capable of predicting variations in area emissions. Assuming the full point source emission rate PDF and the plume instrument’s POD remain stable for a sector and region, the tail of the distribution, observed by an poor sensitivity instrument, should correlate with area emissions. Consequently, the integral of the tail of the frequency distribution of plumes should also correlate with area emissions. (SI Section 1 shows that both plume frequency distribution and area estimates scale with activity, and therefore, with each other.) The 50% POD, P₅₀, for the ANG and GAO instruments used in the Permian survey ranges from 50 to 300 kg h^–1.^29,54 In comparison, most satellite instruments are expected to have poorer detection sensitivities with P₅₀ around 1000 kg h^–1 (although satellites can occasionally identify plumes well below 100 kg h^–1 under favorable observation conditions). Figure 7 shows the temporal distribution of the plume sums from ANG and GAO after applying different emission rate thresholds, including fewer plumes with high emission rates. The overall shape of the weekly sum time series remains similar, even when a threshold of 2000 kg h^–1 is applied, which is the detection sensitivity of Sentinel-2 and Landsat instruments.^50,69

Figure 7.

Temporal sensitivity of plume detections to area emissions at various emission rate thresholds. The panels in the top row show the weekly sum of detected plumes from oil and gas emissions in the Permian Basin for the GAO (A) and ANG (B) instruments. Plumes below threshold values are discarded. Marker colors represent the number of plumes detected each week above the given emission rate threshold. Panel (C) shows the values (eq 4) for the correlation between the sum of plume detections and top-down TROPOMI flux inversion estimates for GAO and ANG. Panel (D) presents the temporal sensitivity (ϕ_T) (eq 4) of plume sums as a function of the emission rate threshold, indicating how sensitive the detected plume sums are at different detection sensitivity thresholds. In Panel (C) and (D), the colors denote the total number of plumes over the 6-week period.

Figure 7C shows the correlation between area and plume sums after applying emission rate thresholds. For the ANG instrument, starting with a zero threshold R²_TS = 0.95 with 1954 plumes, R²_TS (eq 4) remains stable at 0.88, even at a high threshold of 2000 kg h^–1 and only 103 plumes. For the GAO instrument, R²_TS = 1 at zero emission rate threshold, but it shows a marked decline after a 750 kg h^–1 threshold, with only 143 plumes remaining. Notably, an R²_TS of 0.28 is maintained even with 29 GAO plumes at the 2000 kg h^–1 threshold. The sharp decrease in R²_TS for GAO at high thresholds can be attributed to the low sampling of GAO, resulting in fewer plume detections and more diverse observational conditions encountered by GAO.

Figure 7D shows the temporal emission sensitivity metric ϕ_T. We find that ϕ_T is mostly independent of the emission rate thresholds. Surprisingly, ϕ_T for GAO remains stable across thresholds even though the R²_TS values drop. The likely cause is that the errors in the GAO plume sum time series with a lower number of plumes are uncorrelated with area emission variability. Therefore, the errors affect R²_TS and R²_S similarly, and the difference between the two remains unchanged. Overall, our analysis shows that satellite plume instruments, despite their lower detection sensitivity, can evaluate area estimates of oil and gas sector emissions. Our findings align with Lauvaux et al.¹¹ and Ehret et al.,⁵⁰ who also proposed that detected plume emission rates follow consistent global and regional patterns.

5.2. Bayesian Plume Inversion

5.2.1. Weekly Total Permian Emissions

Figure 8 shows the total weekly emission estimates from the plume inversions. We refer to the plume inversions as Plume-EDF inversion and Plume-TRO inversion, which respectively use EDF and TROPOMI emission estimates as priors. The maximum a posteriori (MAP) solutions are termed Plume-EDF and Plume-TRO estimates.

Figure 8.

Weekly methane emission estimates for the Permian oil and gas sector. The dashed horizontal line represents the constant EDF inventory. ‘TROPOMI’ and ‘Plume-TRO’ denote the prior and posterior for the plume inversion performed on TROPOMI emission estimates, respectively. Similarly, ‘EDF’ and ‘Plume-EDF’ respectively represent the prior and posterior for the EDF plume inversion. The DOFS values (orange for Plume-TRO inversion and gray for Plume-EDF inversion) above each bar indicate the level of observational constraint in the inversions. The right-most group of bars gives the mean values across the weeks. Error bars indicate one standard deviation uncertainty.

Degrees of Freedom for Signal (DOFS) values in the figure represent the magnitude of observational constraint in the inversions. For both inversions, the weeks with large DOFS (Oct-11, Oct-18, Oct-25) coincide with the periods when both GAO and ANG instruments were surveying (see Figure 3). During these weeks, the DOFS ranges from 30–38. In the other three weeks, when only one instrument was surveyed, the DOFS ranged from 13–21.

The Plume-TRO inversion’s adjustment to the TROPOMI prior is minor overall, resulting in an increase of only 3% in the 6 week mean (from 462 ± 8 to 472 ± 7 t h^–1). This outcome is expected, given that TROPOMI prior emissions serve to anchor the plume constraint, with τκ quantified from TROPOMI estimates (see eq 3). On a weekly basis, a substantial 13% adjustment is noted for the week of Oct-11 (from 455 ± 23 to 513 ± 18 t h^–1) in the Plume-TRO inversion. Other weeks exhibit smaller adjustments, ranging from −5 to +6%. During the week of Oct-11, the flux inversion by Varon et al.⁹ has the lowest DOFS (2.2 for a state vector with 235 elements); in other weeks, Varon et al.’s⁹ inversion displayed higher DOFS values (2.3–8.3). A common reason for low DOFS is the limited number of TROPOMI observations, often due to cloud cover. Consequently, the TROPOMI inversion estimate was not sufficiently informed by observations and likely remained close to the prior. The fact that the largest adjustments in Plume-TRO inversions occur when TROPOMI estimates are most uncertain (least informed by TROPOMI observations) suggests that plumes improve the accuracy of area emission estimates for this week.

Large adjustments are observed in the Plume-EDF inversion, with plume assimilation increasing the 6-week mean emission rate by 30% (from 294 ± 16 to 380 ± 9 t h^–1). The inversion aligns the posterior Plume-EDF more closely with TROPOMI (and Plume-TRO) estimates, reducing the initial 36% underestimation to 18%. This improvement in the mean is expected, as TROPOMI estimates anchor the plume constraint. Weekly adjustments to the prior EDF inventory are more interesting. Despite using a single τκ value across the 6 weeks (one for each instrument), plume assimilation aligns the weekly emissions with TROPOMI estimates, especially during weeks with high DOFS. For the week of Sep-27, TROPOMI estimates align with the EDF, and the DOFS is minimal, resulting in negligible adjustments by the Plume-EDF inversion. Conversely, during the week of Nov-1, despite much larger TROPOMI estimates, the low DOFS (17) in the Plume-EDF inversion leads to insignificant adjustments. Excluding the week of Nov-1, the plume inversion improves the R² from 0 (constant EDF estimates) to 0.79 (P = 0.04). This demonstrates that the assimilation of plumes can enhance the accuracy of regional total area emission estimates.

5.2.2. Spatial Patterns

Figure 9 shows the mean grid-scale emissions for the Plume-EDF and Plume-TRO inversions. The Plume-EDF inversion increases emissions in most of the grid cells, and the magnitude of emissions becomes similar to the TROPOMI estimates. Both inversions have DOFS hotspots following the spatial pattern of the two major oil and gas production regions: the Delaware (West) and Midland (East) Basins. This is expected, as the plume surveys targeted these major oil and gas production regions. The plume inversion also improves (reduces) the cross-correlation among area emission grid cells (see SI Figure 1). Flux inversions assimilating concentration data induce cross-correlations between grid cells across spatial, temporal, and sectoral domains due to the limitations in resolving the sensitivities across multiple grid cells, often constrained by limited observational data or the resolution of CTM. Given plumes’ near-perfect spatial and sectoral attribution, their assimilation reduces the off-diagonal elements of the correlation matrix, enhancing the spatial specificity of the area emission estimates.

Figure 9.

Six-week mean grid-scale emission maps from plume inversions. Panels (A) and (E) display the priors used in the two inversions, respectively. Panels (B) and (F) show the posterior emissions resulting from the plume inversions, while Panels (C) and (G) show the updates made by the plume inversions. Panels (D) and (H) show the DOFS per pixel, indicating the observational constraints provided by plume data over the six-week period.

6. Discussion

6.1. Plume Constraint on Area Emission Estimates

The plume data record is expanding rapidly, with plumes now regularly observed by numerous aircraft and satellite instruments.⁷⁰ We have presented a method to utilize plume detections to evaluate and inform total regional emission estimates. Using plume data can benefit flux inversion and bottom-up modelers in several ways. First, plume data represents a no-cost data gain for the existing area estimation infrastructure. Plume detections, primarily employed for Leak Detection and Repair (LDAR) methods, serve as a cost-effective addition to provide top-down constraints on area estimates. Second, plume detections provide fine spatial, temporal, and sectoral specificity, which is challenging for conventional top-down methods, which rely on limited-resolution numerical approximation of chaotic atmospheric transport. Third, plume detections provide information on the emission processes, especially in identifying anomalous emissions and their contributions to total emissions, which can improve bottom-up estimates.^8,37

Our study has focused on plume detections from imaging instruments onboard aircraft and satellites. Many surveys use on-ground or aerial in situ instruments to estimate component or facility-scale emissions.^1,71−73 The derived emission estimates from such surveys are similar to the aircraft or satellite plume data from imaging instruments as they provide location, time, and emission rate estimates. Therefore, the gridded sum of emission estimates from in situ surveys can be used to evaluate area estimates or in a plume inversion using the approach presented here.

The plume-based evaluation of area emission estimates and the plume assimilation presented here does not require observation of the full emission rate PDF of the plumes (or point sources). The evaluation of temporal variability in area estimates only requires accounting for the sampling η. For plume inversions , the product τκ needs to be known, additionally. τκ can be obtained by directly comparing the area emissions from a reliable top-down inversion and the sum of plume emission rates after accounting for η, as shown in this study.

A key objective of our investigation was to develop and validate a theory linking plume detections to area emission estimates. By applying this theory to 6 weeks of data from the Permian Basin under ideal conditions, we demonstrated the potential of assimilating plume data to improve emission estimates. Our analysis advances understanding of emission observation methods, though additional factors should be considered when extending the theory to other sectors and regions. Our study focused on the oil and gas sector, characterized by numerous small leaks rather than a few large sources. Extending this approach to other sectors, such as waste management, requires understanding the relationship between plumes and area emissions in those contexts, necessitating further theoretical and empirical analysis.

The effectiveness of plume data assimilation in constraining emissions globally will depend on the availability of plume observations. With the launch of new satellites from GHGSat and Carbon Mapper, as well as the recently launched MethaneSAT and EMIT instruments, the volume of plume data is increasing, enabling more regions to be effectively constrained. Advances in data processing algorithms are also enhancing plume detection capabilities; for instance, Rouet-Leduc and Hulbert⁶⁹ have suggested that Sentinel-2 can detect numerous plumes below 1 t/h by utilizing machine learning across all spectral bands to better distinguish methane spectral signals from surface albedo variations. We anticipate that the detection limits of other instruments with currently underutilized spectral information will also improve in future. Also, within a Bayesian framework, even limited plume data can partially contribute to constraining area emission estimates if model and data uncertainties are properly accounted for. The low amount of plume observations will result in weaker constraints, which will be reflected in larger posterior uncertainties and low DOFS. However, many regions do not have any plume observations to constrain area estimates.

6.2. Co-assimilation of Plume and Concentration Data

Our plume inversion method provides an approach for using fine-spatial-scale plume information from concentration imaging instruments to constrain area emissions. Almost all methane-concentration-imaging area mappers observe methane plumes.⁵¹ For example, TROPOMI methane plumes have been detected from single point sources^11,53 and clusters of point sources.⁴⁹

Using our plume inversion approach, the coassimilation of plume and concentration data is particularly relevant for new and upcoming imaging satellites that will provide concentration constraints and detect plumes with small spatial pixels. For example, the recently launched MethaneSAT satellite instrument has a pixel size of 100 by 400 m and a 200 km swath.⁷⁴ The proposed Carbon-I NASA Earth System Explorer mission will observe at a 400 m spatial pixel in normal (nontarget) operation mode.⁷⁵ These instruments will detect methane plumes and provide top-down concentration constraints for flux inversions. A CTM-based inversion cannot use concentration observation information with a finer spatial resolution than that of the CTM. For instance, if a CTM with a 25 × 25 km² spatial resolution is employed in an inversion assimilating 400 m pixel observations, the inversion will not capture any concentration gradient information at scales smaller than 25 × 25 km². In such cases, the plume inversion approach can maximize the use of information from these satellite observations to inform area emission estimates.

6.3. Periodicity of Oil and Gas Emissions

Some studies have investigated the extent to which area estimates can be accounted for by plume detections,^{5,29,52,56,57} while others have attempted to estimate country-scale emissions using point sources within the oil and gas sector in the USA^6,8,42 and across basins.^36,37 These studies utilize plume detections to refine emission factors and employ a bottom-up extrapolation approach assuming persistence characteristics of plumes. However, the temporal bias of plume detection emissions is not always accounted for, which can potentially result in the overestimation. Oil and gas production emissions have been shown to exhibit periodicity due to activities such as manual liquid unloading and maintenance operations, which typically occur during afternoon working hours.^56,72 Consequently, instruments that favor afternoon observations are likely to exhibit overestimation.

Our analysis indicates a diurnal periodicity in the Permian Basin oil and gas emissions, shown by the high values for the product of plume factors and temporal bias (weekly τκ range 0.89–1.05 for the GAO instrument). As per its definition, τ ≤ 1. We expect true τ of GAO and ANG instruments to be around 0.5 in the Permian Basin, considering Kunkel et al.²⁹ showed that many small plumes are not detected by these instruments. The observed τκ can only be explained by κ > 1. Even though TROPOMI also observes during the afternoon, the region-scale TROPOMI inversion estimates are expected to have a smaller temporal bias since they are sensitive to emission history from the past hours/days.

We suggest future studies to consider emission periodicity when calculating mean emissions using daytime instruments. Periodicity bias can be assessed with bottom-up data or through an optimal plume survey strategy. For example, continuous day-night monitoring in the Permian Basin using aerial LIDAR or in situ instruments can capture emission periodicity.

6.4. Comparison of Plumes from Different Instruments

Our work highlights issues with comparing plume emission rates from instruments with different pixel sizes, especially in dense point-source emission fields like oil and gas production basins. Coarse spatial pixel-size instruments capture emissions from a large cluster of point sources together, complicating the direct comparison with plumes from fine pixel-size instruments (Figure 1 and 2). The plume clustering effect is also relevant for comparing emission rates of trace gases like CO₂ and NO₂.^76,77 For instance, CO₂ plumes observed by coarse-resolution satellites (e.g., OCO-3) cover larger areas and show higher emission rates than those observed by fine-resolution satellites (e.g., PRISMA, EnMAP, EMIT) that observe plumes from specific point sources like a power plant’s smokestack.^76,78 We suggest future research to investigate and account for the plume clustering effect on a broader spectrum of methane emission sectors and other trace gases (CO₂, CO, NO₂, etc.) that are observed as plumes and area emission estimates.

Data Availability Statement

The plume inversion code developed in this study and the Permian Basin methane emission data used are freely available at: https://zenodo.org/records/15066296.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.est.4c07415.

• The file includes the following sections: (1) derivation of statistical relationship between area estimates and plume sums. (2) Bayesian assimilation of plume observations. (3) Description of area estimates of emissions and plume observations data sets. (PDF)

Author Contributions

S.P. and J.W. designed the study. S.P. formulated the theoretical framework and performed the analysis. J.W., K.B., and D.J. supported and discussed the analysis. D.V. provided the Permian Basin TROPOMI inversions, and D.C. provided the plume data. All authors participated in the discussion and contributed to writing the manuscript.

The authors declare no competing financial interest.