Figure 1 outlines the developed protocol for creating a measurement-based inventory from source- or site-resolved measurement data. For the ideal scenario of a comprehensive measurement survey using a perfectly accurate and infinitely sensitive instrument, all sources would be captured such that the emissions inventory would be the sum of all directly measured emissions. In practice however, the finite detection sensitivity of methane-sensing instrumentation necessitates a piecewise approach considering two nonoverlapping subsets – measured/measurable and unmeasured/unmeasurable sources – that sum to the whole. Measured sources are those that were detected and quantified at the surveyed sites as well as sources that would be detected/quantified at sites not included in the survey sample. By contrast, unmeasured sources are those that were not successfully detected during the survey and those that would not be detected/quantified at sites not included in the sample.
Importantly, the diverse facility types within the upstream oil and gas sector (e.g., isolated wells, multi-well batteries, compressor stations, gas plants, etc.) are treated as separate strata within the overall sample; Fig. 1 is thus separately applied in parallel to each stratum as defined in Table S1 of the Supplemental Information (SI) for the demonstration inventory in BC along with associated sample and population sizes for each. Aggregation of like entities into homogeneous strata tends to reduce the variance of desired statistics, improving the precision in each stratum’s calculated mean emission rate (i.e., emission factor) and total emissions (i.e., emissions inventory). This approach can also permit stratum-dependent methodologies leveraging prior information about the strata – e.g., pneumatic equipment at gas plants in BC are almost exclusively air-driven and may be ignored in the methane inventory. Finally, this approach provides the relative contribution of each stratum to the whole, which is important data for regulation and mitigation. While the present demonstration of this approach uses aerial measurement data collected using Bridger Photonics Gas Mapping LiDAR (GML), the protocol is generally applicable to any technology with well-characterized probabilities of detection (POD) and quantification uncertainties25 and sufficient spatial resolution to resolve individual facilities.
Protocol for Quantifying Measured Sources and Uncertainties
As outlined in Fig. 1a and more fully detailed in the SI, the measured source inventory calculation takes pass-by-pass aerial measurement data from surveyed sites, introduces known measurement uncertainties and detection sensitivities25 via Monte Carlo and Bayesian analysis, and scales via bootstrapping to consider sites not included in the sample. This approach solves three key challenges. First, the joint Monte Carlo and Bayesian approach (see Section S2.1) provides a formal framework for objectively considering any “missed” detections of a source seen in one or more other passes of the aircraft, noting that this could be due to both variability/intermittency of the source and/or the finite detection sensitivity of GML. Notably, this approach allows explicit consideration of the condition-specific probability of detection during each measurement pass along with available information about a source from all passes where it had a potential to be measured. Second, the Monte Carlo analysis robustly considers the source quantification uncertainty during each pass, leveraging detailed uncertainty models for the aerial technology25, permitting direct analysis of measurement uncertainties at the source, site, and inventory level. Third, the mirror-match bootstrapping technique26,27 enables robust scaling of emissions in each sample stratum to the population in a way that considers the actual distribution of emissions at sites in the stratum (which are generally non-smooth and highly skewed) as well as finite population effects (which are critically important since the population of facilities and wells in each stratum is finite, and the size of the sample can be large relative to the population, see Table S1 of the SI). Stated in terms of a specific example, it would not be reasonable to consider methane emissions at a gas plant as indicative of emissions at a well site when developing an inventory, which shows the importance of stratified sampling. Even at the source level, where both types of sites may have some similar equipment, it is also unlikely these would be from equivalent populations given expected differences in controls, sizing, and throughput. Conversely, within any region of interest such as the province of BC, the total population of gas plants is finite (60 active facilities in 2021) and “standard” statistics based on assumed (non-Gaussian) distributions for an infinite population are not accurate or relevant. Notably, the implemented mirror-match bootstrapping approach overcomes these challenges to permit independent and robust analysis of sample size uncertainties for each stratum and for the total inventory.
Figure 2 illustrates the power of this approach in producing a measured-source methane inventory using the present analysis of BC, Canada as an example. The total measured inventory of 112.2 kt/yr is computed by summing the measured inventory for each unique strata over BMC = 104 times BBS = 104 estimates, and reveals overall uncertainties of − 18% to + 21% at 95% confidence. Interestingly, despite the relatively large sample sizes (see Table S1), the combined uncertainties are still dominated by sample size effects. A key innovation of this approach is a robust framework for considering sample size requirements in future inventory studies and regulated monitoring, reporting, and verification (MRV) efforts.
Figure 2b demonstrates how the method can also be used to calculate separate inventory uncertainties for different facility types (strata) and their relative contributions to the overall uncertainty of the measured portion of the inventory. The bars of Fig. 2b are shaded by the percentage of each stratum’s population included in the sample, which highlights important effects that may not be automatically anticipated. For example, while the relatively large uncertainty contribution of compressor stations might be expected from the comparatively low sample coverage of 18% for that stratum, the large uncertainty for gas plants relative to its magnitude is potentially unexpected, especially the large sample size uncertainty given the 77% sample coverage. This can ultimately be explained by the strongly skewed distribution of sources at gas plants, where parallel root cause analysis28 has shown that emissions tend to be driven by controlled tank sources that generally do not emit but can emit large volumes when they do. Conversely, uncertainties at off-site gas wells are nearly equally affected by quantification uncertainty and sample size uncertainty despite lower sample coverage (9%) implying less internal variability within the off-site gas well stratum. Most importantly, the results of Fig. 2b demonstrate how the presented protocol yields useful data to optimize the design of future measurement campaigns to maximize precision and minimize sampling effort. It should also be noted that any temporal variability among sites in each stratum, in addition to being empirically considered through measurement flights over separate days each with potentially multiple passes, should manifest as increased variability in emissions among sites in the sample and thus is also inherently captured in the uncertainty analysis. This is further analyzed in the Discussion below.
Protocol for Estimating Unmeasured Sources
The preceding measured source protocol quantifies the contribution of all sources that are detected and quantified during at least one flight pass. However, due to source intermittency and the probabilistic and finite sensitivity of aerial methane-detection technologies, some quantity of sources may not be detected during any flight pass of the survey. Depending on the sensitivity of the employed aerial technology and the jurisdiction’s underlying source distribution, these unmeasured sources may be significant and must be considered during inventory development. Referring to Fig. 1b, this is possible via a parallel Monte Carlo simulation considering site/condition-specific POD25 using “bottom-up” equipment count and measurement data from prior studies (e.g., refs 29–33) as inputs. This new “unmeasured source” protocol allows robust derivation of stratum-dependent, average, emission factors for unmeasured sources on a per-site basis.
Briefly, for an aerial survey of \(N\) unique flight passes over a source, where each pass has a unique POD that depends on the conditions (e.g., wind and altitude) and source rate at the time of the pass, the source is unmeasured if it is probabilistically missed during all \(N\) passes. This problem is ideally suited to Monte Carlo analysis as shown in Fig. 1b and more fully detailed in S2.2 of the SI. Inputs (shown in red) include the actual empirical distribution of the number of flight passes over a source and the distributions of wind speeds and altitudes from each pass of the survey; continuous POD data from the aerial technology25; and relevant bottom-up data from the literature for the distribution of potential sources near and below the aerial technology’s sensitivity limit. These bottom-up feedstock data may include measurement data from surveys using more-sensitive technologies and/or the combination of counts and typical (manufacturer-rated) emissions of underlying equipment, similar to those used to derive the emission factors underpinning traditional bottom-up inventories.
For the presently derived inventory for BC in 2021, supplemental feedstock data were sourced from a ground survey of 149 unique sites (including 62 facilities and 205 wells) in BC performed in 201832. This data set includes 1) estimated emission rates from non-pneumatic equipment detected by optical gas imaging and measured where possible using Hi-Flow sampling, 2) counts and identification (manufacturer and model) of pneumatic equipment, and 3) estimated vent rates for identified pneumatics based on prior field measurements and manufacturer data. More generally, in the absence of region-specific feedstock data, other general data sets (such as refs. 29–31, 33–37) may be used as in the work of Rutherford16. The Monte Carlo analysis then outputs final average site-level emission factors which are applied to the stratum’s population to yield the unmeasured inventory for the stratum, optionally parsed by non-pneumatics (orange, see section S2.2.1 of the SI) and pneumatic instrument/pumps (gray, see section S2.2.2 of the SI). Detailed results of the unmeasured source analysis for BC are included in the SI.