A Review of Source-Term Estimation for Continuous Methane Monitoring: From Data Acquisition to Modeling and Estimation

Abstract

Accurately quantifying methane emissions in the oil and gas industries is essential for meeting global climate targets. Combining fixed continuous monitoring systems with source-term estimation (STE) offers a promising pathway. This article provides a systematic review of the technical framework, comprising two core steps: data collection and inverse modeling, with the aim of identifying key technological bottlenecks and outlining directions for future development. The main conclusions are as follows: (1) There is a fundamental misalignment between prevailing sensor-deployment strategies and the ultimate inversion objective. Current optimization criteria primarily seek to maximize detection probability while neglecting their direct coupling with the minimization of uncertainty in the inferred parameters, which constitutes a central bottleneck limiting overall system accuracy. (2) Model and algorithm selection involves pronounced trade-offs and interdependencies. The study identifies an inherent contradiction between the high fidelity and computational efficiency of dispersion models, which directly constrains the choice of estimation algorithms. Moreover, Bayesian approaches offer clear advantages over deterministic optimization when confronting ill-conditioned inverse problems arising from sparse data because they accommodate prior information and enable uncertainty quantification. On the basis of these findings, future research should focus on developing sensor-deployment theory oriented toward inversion accuracy, building high-fidelity surrogate models that balance accuracy and efficiency, and advancing probabilistic inversion methods for multisource, sparse data. These recommendations are intended to guide the large-scale implementation of fixed continuous monitoring systems in the oil and gas sector and to accelerate technological innovation and practice in the green, low-carbon transition.

Introduction

Methane is a potent greenhouse gas whose global warming potential is 27.9 times that of carbon dioxide over a 100-year horizon and 81.2 times over 20 years. In the oil and gas industry, methane emissions are a major environmental and safety concern and have been a principal driver of the recent global rise in atmospheric methane. The oil and gas sector is a major source of anthropogenic methane, with emission sources that are widely distributed in space and variable in time, producing complex spatiotemporal patterns. − Therefore, accurately monitoring, identifying, and quantifying methane emissions from oil and gas facilities has become a central challenge for climate mitigation and for ensuring safe operations across the industry.

As countries adopt new policies and increasingly stringent emission-reduction targets, − methane measurement techniques and accounting approaches must become more accurate and diversified to meet varied regulatory and operational needs. Existing methods for methane emissions accounting fall into two broad categories: bottom-up and top-down. Bottom-up methods, such as flux chambers , and the high-flow sampler (HFS) method, provide accurate component-level emission factors but offer limited temporal representativeness. Top-down approaches include satellites, , aircraft, , drones, , and vehicle-based mobile monitoring, , which can estimate facility-level emissions and operate across a wide range of spatial and temporal scales (Figure ). It should be noted that, although these observation methods can support station-level emission assessment, they differ substantially in the type and granularity of information they can resolve. Satellite and aircraft monitoring typically provides broad spatial coverage and is well-suited for identifying large emissions and anomalies at regional or station scales. However, constraints in spatial resolution and viewing geometry make it difficult to deliver reliable localization for specific leak points within a station. In contrast, drone- and vehicle-based monitoring generally offer higher spatial resolution and can detect smaller emission signals, but they remain short-duration scans or snapshot observations; as a result, their ability to disaggregate emissions and attribute them to individual sources is still limited. Consequently, mismatches in the temporal and spatial representativeness of top-down snapshots can lead to substantial discrepancies between emission inventories and actual emissions. ,

1.

Multiscale measurement of oil and gas industry sites. Original illustration (not a photograph) was created by the authors.

By contrast, fixed continuous monitoring systems , can deliver near-real-time, site-scale coverage of emissions and can capture highly dynamic, short-duration events, thereby complementing periodic inspections. Current deployment modes include: (1) in situ downwind measurements using fixed concentration sensors; (2) open-path concentration measurements using laser sensors; and (3) tall-tower measurements using the micrometeorological eddy-covariance method. Among these approaches, point-sensor networks are widely viewed as the most feasible option for large-scale deployment in the oil and gas sector because of their scalability and cost advantages; accordingly, they are the primary focus of this article.

At the policy level, adoption of this technology is accelerating. The U.S. Environmental Protection Agency’s 2023 final rule underscores strengthening methane leak detection through innovative technologies and explicitly includes satellites, aerial monitoring, and continuous monitoring systems as compliance options, allowing companies to use continuous monitoring technology instead of periodic inspections for the first time, and proposing long-term and short-term action thresholds for leaks of different scales. Under the U.S. EPA’s Subpart OOOOb rule, a detection event is triggered when continuous monitoring data exceed the alarm threshold, and emission rates are estimated using the median of multiperiod measurements. In Canada, the revised Regulations Respecting Reduction in the Release of Methane and Certain Volatile Organic Compounds (Upstream Oil and Gas Sector) formally establish continuous monitoring systems, for the first time, as a compliance pathway that can operate in parallel with traditional LDAR. This change represents a major shift in Canada’s regulatory approach from periodic inspections toward near-real-time monitoring, offering operators more flexible options for demonstrating compliance. China’s Action Plan for Methane Emission Control calls for building an integrated sky and ground monitoring system and emphasizes fixed ground monitoring. Taken together, these policies indicate that fixed continuous monitoring is becoming an important tool for meeting regulatory requirements and improving data transparency.

However, recent performance estimations reveal wide variation in the detection rates and quantification accuracy across continuous monitoring solutions. Controlled-release tests report detection probabilities as low as 30% and as high as 90%, with quantification errors ranging from −40% to 90%. , These findings highlight several technical bottlenecks: insufficient detection reliability, instability in source-localization accuracy, and large quantification uncertainty under sparse sensor coverage.

Methodologically, inferring the location and intensity of emission sources from spatial point concentration measurements constitutes a severely ill-posed inverse problem. Reliable source-term estimation (STE) requires coupling limited observations with the governing physics of atmospheric dispersion models and employing statistical inference or optimization to retrieve source parameters. However, practical applications face several challenges: sparse data arising from limited sensor deployments; dispersion models whose computational demands preclude real-time operation; and the propagation of uncertainty in scenarios with multiple sources.

Building on the preceding discussion, this study addresses the key challenges of achieving precise quantification and localization in automated methane monitoring within the oil and gas industry. Its primary objective is to introduce STE methods and propose a standardized framework for fixed continuous monitoring, thereby providing a reusable technical paradigm for industrial applications. The second objective is to systematically examine the two core factors that constrain the accuracy of STE, namely, data collection and modeling inference, to clarify the advantages, limitations, and development trends of existing research and to reveal optimization pathways for cross-domain technology integration. The ultimate goal is to guide the large-scale implementation of fixed continuous monitoring systems in the oil and gas sector, enhancing detection capabilities and quantification accuracy. This systematic review will assist business decision-makers and engineering practitioners in selecting the most suitable solutions for their facility characteristics and regulatory requirements, foster the industrialization of fixed continuous monitoring, and ultimately advance technological innovation and practice toward a greener, low-carbon transition in the oil and gas industry.

STE Framework

The fixed continuous monitoring system enables source-term assessment for methane emission detection, localization, and quantification in the oil and gas industry through minute-level or even higher-frequency concentration observations combined with corresponding meteorological data. Figure illustrates the general technical framework of a continuous monitoring system. Acquiring measurement data is the foundational step of the estimation process, achieved by deploying sensors within the monitoring domain to collect high-quality concentrations and supporting meteorological information. A dispersion model is then applied to simulate the atmospheric transport of methane and generate theoretical predictions of the concentration fields. By formulation of cost functions that link measured and simulated concentrations, optimal solutions are obtained through optimization or probabilistic inference methods.

2.

General technical framework for continuous monitoring system.

Mathematical Model

In the forward dispersion process, known source parameters (position, intensity, and time) can uniquely determine the concentration field distribution through the convection–diffusion equation:

$$\frac{\partial C}{\partial t}+\nabla ·(\mathbf{u}C)=\nabla ·(D\nabla C)+S$$ 1

where C is the concentration of atmospheric pollutants at the sensor position observed by the sensor, u represents the three-dimensional space wind speed vector, D is the dispersion coefficient matrix, S is the emission rate, ∇ is the divergence of vector field, and ∇C is the concentration gradient. Given different assumptions, the corresponding atmospheric dispersion model can be derived.

Since the location and intensity of emission sources are unknown, the cost function must be evaluated multiple times under various assumptions about the locations and intensities of emission sources within the monitoring area during the actual calculation process. There are two primary methods for describing source–receptor relationships: the forward model and the backward model. The forward model (source oriented) focuses on solving the concentration of the monitoring receptor with a given source parameter, covering all of the potential values of the source parameter variables in the minimization of multiple solutions, which will inevitably lead to a waste of computing resources and an extension of the solution time. Backward model (receptor-oriented) is a more computationally efficient method. The method uses the sensor as the source, reversing wind speed, wind direction, and other meteorological variables. Assuring that the measured value of m monitoring points is c_i , the monitored pollutants are generated by mutually independent emission sources, and the linear relationship between the concentration of monitoring points and the intensity of emission sources can be expressed as the adjoint equation. By calculating the adjoint equation, the running times of the potentially expensive dispersion model can be significantly reduced. Generally, the calculation times of the adjoint equation are equal to the number of monitoring points because a single adjoint matrix can be used to test the cost function of multiple source parameters.

$$\mathbf{c}=\mathbf{A}\mathbf{q}$$ 2

$$\mathbf{c}=\left[\begin{array}{l}{c}_1\\ c_2\\ ⋮\\ c_m\end{array}\right],\mathbf{A}=\left[\begin{array}{llll}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right],\mathbf{q}=\left[\begin{array}{l}{q}_1\\ q_2\\ ⋮\\ q_n\end{array}\right]$$ 3

where the adjoint coefficient A is calculated through the dispersion model.

Technical System of STE Method

Based on the above technical framework, the successful implementation of STE relies on two core components: data acquisition and modeling estimation.

Data Acquisition: Sensor Performance and Deployment

Data acquisition is the foundational step in the STE. Theoretically, if sensors cannot effectively measure concentration information, all inversion algorithms become meaningless, as the quality of the measurement data directly sets the upper limit of subsequent modeling and inference performance. Sensor selection determines the accuracy, detection limit, and response speed of the observations, thereby influencing both the range of detectable emission events and overall data quality. More importantly, as shown in , when the number of monitoring points m is smaller than the number of emission sources n, the inverse problem of STE becomes ill-posed. Observation data must therefore satisfy not only the basic solvability requirement in terms of quantity but also possess sufficient information content in terms of quality to ensure stable inversion of source parameters. The number and spatial arrangement of sensor deployments determine the information content and condition number of the adjoint coefficient matrix A, which in turn affects the numerical stability and solution accuracy of the inversion problem.

Compared with other monitoring technologies, fixed sensors are difficult to relocate once they are deployed. Owing to their high deployment and maintenance costs, as well as safety and terrain constraints at oil and gas facilities, the data collected by each sensor are extremely valuable. Therefore, it is essential to achieve an optimal balance among the number of sensors, monitoring coverage, and information quality, which represents the primary technical challenge for STE.

Modeling Estimation: Diffusion Models and Estimation Algorithms

The modeling and inference process establishes the source–receptor relationship through numerical computation methods and performs the inversion of the source parameters. This process comprises two modules: a dispersion model and an estimation algorithm, which must work in concert to achieve accurate and efficient STE.

The dispersion model is responsible for computing adjoint coefficient matrix A, which characterizes the physical relationship between emission sources and monitoring points. By applying different assumptions, the corresponding atmospheric dispersion models can be derived from the convection–diffusion equation. Model selection involves a trade-off between accuracy and computational efficiency. Holmes classified various types of dispersion modelsfrom simple box models to complex computational fluid dynamics (CFD) modelsand evaluated their applicability under different environmental conditions. High-fidelity CFD models can accurately describe complex terrain and turbulent flow effects but have high computational costs, making the real-time implementation difficult. In contrast, simplified Gaussian dispersion models are computationally efficient but exhibit limited accuracy in complex scenarios. This trade-off directly affects the engineering feasibility of the STE system.

The estimation algorithm determines the source parameters by constructing a cost function and applying numerical optimization or probabilistic inference methods. Algorithm design must balance computational efficiency, numerical stability, and the ability to quantify uncertainty. In particular, for multisource separation problems, algorithmic stability and the capacity to handle physical constraints become key performance indicators.

Technical System Integration

The effective implementation of a continuous monitoring system requires the integration of two core technical components: data collection and modeling inference. The performance and spatial configuration of the sensor network determine the theoretical upper limit of the available information, whereas the algorithm design for modeling and inference determines the actual efficiency of information utilization.

Existing research often examines these two technological systems separately. Sensor-deployment optimization primarily focuses on maximizing the detection rate of emission events with limited attention to its influence on the accuracy of source parameter inversion. Meanwhile, dispersion modeling and algorithm design typically assume a predetermined sensor layout without fully exploiting the potential of layout optimization. This technological fragmentation constrains overall system performance improvement and constitutes a major bottleneck in the current development of STE technology.

Based on the above analysis, the structure of this article is arranged as follows. The section “Data Acquisition: Sensor Networks and Deployment” focuses on data collection techniques, including sensor types, measurement performance analysis, and spatial deployment optimization strategies for sensor networks. It discusses how to build high-quality observation networks under cost constraints to improve the accuracy of the STE. The section “Diffusion Model and Estimation Algorithm” presents the theoretical foundations and application characteristics of dispersion models, as well as recent advances in estimation algorithms. It compares and evaluates the engineering applicability of different model–algorithm combinations in terms of accuracy, real-time performance, and stability. Finally, based on a comprehensive examination of the entire technical chain, this article summarizes the core findings, identifies key bottlenecks in the current technology system, and proposes directions for future research. Although this review focuses on the automatic positioning and quantification solutions for fixed continuous monitoring of oil and gas industry stations, given the significant interdisciplinary nature of the technology system involved, some methods and technologies are derived from nonoil and gas scenarios or research at different spatial scales. The positioning in this review is the methodological background and transferable ideas, which do not mean that these methods have been validated in station-level applications or can be directly copied. This feature of cross-disciplinary technology integration constitutes an important dimension of the present review.

Data Acquisition: Sensor Networks and Deployment

Sensor Type and Performance

Recent years have seen significant advances in methane sensing, including metal-oxide semiconductor (MOS) sensors, nondispersive infrared (NDIR) sensors, tunable diode laser absorption spectroscopy (TDLAS), and cavity ring-down spectroscopy (CRDS). Figure shows schematics of the representative sensor types. Although these technologies support different monitoring approaches, their detection principles and performance characteristics inform sensor selection for fixed continuous monitoring systems. Table summarizes the detection principles, performance, and applications of these sensors.

3.

Schematics and working principles of gas sensor types, including: (a) NDIR sensor. Reprinted with permission from ref . Copyright 2023 Elsevier. (b) N- and P-type MOS sensors. Reprinted with permission from ref . Copyright 2022 Elsevier. (c) TDLAS sensor. Reprinted with permission from ref . Copyright 2025 American Chemical Society. (d) CRDS sensor. Reprinted with permission from ref . Copyright 2020 American Chemical Society.

1. Summary of Methane Sensor Types, Principles, and Detection Performance.

sensor type	principle	detection performance	application
NDIR	uses a broadband infrared source; a band-pass filter selects the band containing CH4 absorption peaks for measurement	precision: 1 ppm
		range: 0.1–5000 ppm
		resolution: 0.1 ppm
MOS	target gas reacts on the surface of a metal-oxide semiconductor, causing a change in conductivity	precision: ±1 ppm (<28 ppm)
		±31 ppm (<1000 ppm)
		range: 2–1000 ppm
		resolution: 1 ppm
TDLAS	a narrow-line width laser diode scans a single high-resolution absorption line; the peak absorption at the line center is compared with the zero level on both sides	precision: 0.125 ppm
		range: 0–100 ppm
		resolution: 0.1 ppm
CRDS	obtains the absorption spectrum by measuring the ring-down time of a light beam transmitted through an optical resonant cavity	precision: 1 ppb
		range: 1.5–30 ppm
		resolution: 1 ppb

High-precision optical sensors such as CRDS provide accurate, stable, and highly selective concentration data. However, the initial deployment cost is high, which limits deployment density and may fail to capture spatially complex leakage patterns. Low-cost sensors, such as MOS, enable high-density networks, yet they typically have high detection thresholds and exhibit time-varying systematic drift. Such drift is very difficult to filter or correct in downstream models and algorithms. TDLAS and NDIR sensors offer a practical compromise between deployment cost and measurement accuracy for projects with limited budgets, although operators must recognize that their data performance is lower than that of high-end sensors.

The single-point performance of sensors is a prerequisite for accurate measurement, but for spatial dispersion processes, high-quality single-point data are still insufficient to support evaluation. The effectiveness of monitoring networks depends more on the spatial layout of the array. When monitoring targets (such as detection coverage) and cost constraints are determined, maximizing STE performance can be attributed to the joint optimization of sensor types, quantities, and locations to improve overall performance with limited resources. The next section will discuss deployment optimization methods and algorithms and explain their key role in improving the performance of STE systems.

Sensor-Deployment Optimization

Continuous monitoring, as an emerging technology for methane emission regulation in the oil and gas industry, has not yet been extensively studied, in terms of sensor-deployment optimization. Existing research primarily focuses on maximizing the detection rates. Chen et al. demonstrated that the number of sensors exerts a greater influence on the overall detection probability of emission events than the individual sensor detection threshold. Klise et al. developed the open-source Python package Chama, a framework that integrates meteorological and emission data as prior information to perform emission simulations. It combines sensor detection thresholds and cost constraints to determine the optimal sensor placement through mixed-integer linear programming (MILP).

Building on Klise et al.’s foundational work, Zi et al. examined the impact of environmental wind uncertainty on sensor placement strategies and adopted a distributed robust optimization (DRO) approach to enhance the detection robustness of sensor networks. Patel and Zenker proposed a probabilistic hierarchical monitoring sensor placement method that accounts for both sensor accuracy and cost, achieving more than a 2-fold increase in monitoring coverage with the optimized network. Jia et al. developed a modular framework for optimizing the deployment of fixed continuous monitoring sensors in the oil and gas industry. The framework includes five key steps: (1) simulating gas emission scenarios at monitoring sites, (2) considering terrain constraints to define candidate sensor locations, (3) calculating methane concentrations at sensor positions, (4) evaluating sensor detection rates, and (5) applying genetic algorithms combined with Pareto optimization to maximize monitoring performance. This framework has been successfully implemented and validated in oil and gas field applications (Figure ). However, as outlined in Bell’s standardized testing protocol, the detection rate of methane emission events remains the most fundamental indicator for evaluating fixed continuous monitoring frameworks. Existing sensor optimization methods mainly focus on improving event detection rates without considering their potential contribution to enhancing the accuracy of STE, specifically, the inversion of emission source location and intensity.

4.

Representative studies on sensor-deployment optimization for methane continuous monitoring systems in the oil and gas industry, including: (a) Chama optimization results for different emission levels and sensor budgets. Reprinted with permission from ref . Copyright 2024 Institute of Physics. (b) application scenarios and optimization results of a modular framework for optimized deployment. Reprinted with permission from ref . Copyright 2025 American Chemical Society.

The sensor-deployment optimization problem typically aims to maximize the representativeness of pollutant concentrations across the target area through a network of monitoring sensors, thereby enabling optimized spatial layouts and adaptive adjustment strategies for monitoring stations. Based on the existing research, the optimization criteria for sensor deployment can be summarized into three categories of goal-oriented design principles.

Monitoring Coverage Criteria

The core objective of this design criterion is to maximize monitoring area coverage and ensure complete coverage of potential emission sources through an optimized spatial distribution. This criterion is primarily applied during the initial layout stage of sensor networks, with the aim of identifying possible concentration increases and providing regional alerts. Most existing continuous monitoring systems in the oil and gas industry are based on this principle; however, for STE, their monitoring accuracy remains insufficient. Legg et al. , used FLACS software to generate gas dispersion data and developed a stochastic optimization process that incorporates conditional risk values to guide sensor placement, minimizing the expected detection time while ensuring adequate coverage. Rad et al. addressed the dual optimization problems of maximizing sensor coverage and minimizing detection time using two forms of extended integer linear programming, introducing a multilevel voting mechanism to enhance sensor placement effectiveness. Sui et al. combined hierarchical clustering with optimization algorithms to develop a full-coverage optimization method for leak sensors tailored to urban gas pipelines, based on the dispersion characteristics of gases in various soil types. The method’s superiority was verified through both simulation and field test results.

Quantity Optimization Criteria

The core objective of this design criterion is to achieve an optimal balance between cost-effectiveness and accuracy, ensuring that the concentration distribution of specific atmospheric pollutants within the monitoring area is precisely represented, while minimizing redundant sensors to reduce overall costs. Abida et al. designed a sensor network based on physical criteria incorporating transport models to monitor accidental releases from French nuclear power plants and highlighted the critical role of cost functions in sensor network design. Kouichi et al. proposed a data assimilation optimization method that integrates a simulated annealing algorithm with CFD modeling to optimally reduce the number and size of existing monitoring networks in urban environments. This method was validated through 20 field experiments using the Mock Urban Setting Test (MUST) tracer. Ning et al. collected concentration data using both uniformly and nonuniformly distributed sensors and proposed a sampling theory with a limited innovation rate to reduce the number of sensors and overall costs. Finally, a dispersion inverse problem model was established to estimate leakage source parameters under both instantaneous and continuous point source conditions. Guided by risk information, Dong et al. deployed sensors in high-risk areas to capture more information and determined sensor placement sequences through similarity-based redundancy detection to reduce deployment costs.

This type of design criterion assumes that the sensor network can fully represent the spatial concentration distribution and employs heuristic algorithms to reduce monitoring points in areas of high network efficiency while increasing them in areas of low efficiency. Consequently, this approach depends on the infrastructure of well-established sensor networks and is mainly used for iterative upgrades of existing systems, making it less applicable to sparse or newly deployed networks.

Information Entropy Criterion

The third type is the dynamic redeployment criterion based on information entropy. , This approach applies the principle of maximizing information entropy to globally optimize sensor locations, overcoming the limitations of existing networks, and maximizing the information obtained from a limited number of sensors. It is particularly suitable for continuous fixed monitoring scenarios of methane emissions, where its main advantage lies in determining the optimal sensor configuration according to STE objectives while integrating data assimilation and model correction techniques.

Keats et al. proposed an information theory-based approach that strategically places an additional sensor to maximize the effective information contained in the posterior probability distribution of source parameters. The accuracy of the estimated source position and intensity before and after the addition of sensors was experimentally compared to validate the method. Lin et al. employed Bayesian optimization to identify the optimal sensor position within a continuous design space while reducing the number of lower-bound estimations, providing numerical results for both synthetic and real-world data sets. The results demonstrate that the proposed method effectively captures dependency relationships and infers monitoring information. Ngae et al. applied a renormalization inversion method combined with an entropy-based cost function to quantify the amount of information provided by sensor networks. The comparison between prior and nonprior designs showed that sensor networks optimized under entropy criteria can accurately retrieve unknown emission sources in urban environments. Tornyeviadzi et al. proposed a sensor preselection algorithm based on community detection and maximum entropy computation to reduce the search space in pressure sensor placement problems. Their findings indicate that only 21 pressure sensors are required to cover 95.45% of the water distribution network. Although the research object is the water supply network, this article cites it as a methodological reference for sensor deployment optimization. Jia and Kikumoto determined the optimal sensor configuration for the STE problem in a block array model under stable meteorological conditions, using the joint entropy of concentration information as the objective function. Building on this work, Liu and Li proposed a new sensor configuration design method that weights the joint entropy of multiwind-direction concentration information to formulate a cost function, which is then minimized using a simulated annealing (SA) algorithm. The optimized sensor deployment significantly enhances the estimation accuracy of the source location and intensity compared with traditional uniform sensor configurations.

Summary

The shared objective of these three categories of criteria is to enhance the monitoring system performance or reduce costs while maintaining sufficient monitoring effectiveness. However, their methodological focuses differ significantly. Specifically, geometric criteria emphasize the completeness of spatial coverage, quantity optimization prioritizes deployment cost efficiency, and information entropy criteria pursue optimal information acquisition. This classification framework provides distinct technical pathways suited to various project stages, including new construction, system upgrading, and network reconstruction. Furthermore, this broadens the theoretical foundation of sensor-deployment strategies from multiple perspectives. Table presents the classification and feature comparison of the sensor-deployment optimization criteria.

2. Classification and Feature Comparison of Optimization Criteria for Sensor Deployment.

criterion	solution method	evidence type	ref
monitoring coverage	mixed-integer linear programming (MILP)/a stochastic programming formulation	simulation
	mixed-integer linear programming (MILP)	simulation
	multilevel voting (MLV) + integer linear programming (ILP)	simulation
	distributed robust optimization (DRO)	simulation
	Gas + PORSS	simulation + experiment
	hierarchical clustering + ant colony optimization (ACO)	simulation + experiment
quantity optimization	CFD + simulated annealing (SA)	experiment
	finite rate of innovation (FRI)	simulation
	risk information (RI) + redundancy detection	simulation
information entropy	Bayesian adaptive exploration (BAE)	experiment
	Bayesian optimization	simulation + actual data
	information entropy + Bayesian + SA	simulation
	joint entropy + Bayesian + SA	simulation
	joint entropy + Bayesian + SA	simulation

Fixed continuous monitoring in the oil and gas industry typically serves objectives on multiple time scales. In the short term, it is used to detect unexpected or previously unknown leaks and provide early warnings to enable rapid response. Over the long term, it supports the quantification of cumulative emissions within the monitoring area. However, existing single-criterion optimization approaches face significant limitations due to dynamic variations in meteorological parameters throughout the year. Although deployment strategies based on information entropy can enhance inversion accuracy, they rely on static meteorological assumptions, such as annual average wind speed and direction. This reliance makes them unsuitable for adaptation to time-varying environmental wind conditions. Specifically, persistent reverse-dominant wind directions can create monitoring blind spots. Conversely, criteria based on geometric coverage can ensure spatial completeness but often fail to maximize quantitative performance. Therefore, we argue that a multicriteria optimization framework represents the key direction for future research. Such an approach can balance the spatial coverage and functional performance of monitoring networks under varying seasonal wind fields, thereby supporting continuous and accurate traceability of methane emission traceability.

Diffusion Model and Estimation Algorithm

Dispersion Model

At present, extensive research has been conducted both domestically and internationally on the forward simulation of methane emission dispersion. This effort has led to the development of a wide range of models and software tools aimed at improving the accuracy of gas dispersion predictions. Traditional approaches, such as Gaussian and Lagrangian models, CFD models, and artificial intelligence techniques, are widely applied to gas dispersion simulations across various fields and application scenarios. These AI techniques specifically include machine learning and deep learning methods. Table provides a comparative analysis of the key characteristics of different forward dispersion models.

3. Comparative Characteristics of the Forward Dispersion Models.

type	advantages	limitations	ref
Gaussian plume	(1) closed-form and fast; (2) easy to implement; (3) good for online screening and baseline estimation; (4) widely used in early STE studies	(1) steady, homogeneous winds only; (2) weak near-surface; (3) large errors under low wind/near field and complex terrain/building flows; (4) smooths intermittent releases	−
Gaussian puff	(1) handles instantaneous/intermittent releases and time-varying winds; (2) time dependence helps event detection; (3) efficient	(1) multipuff superposition and boundary handling are complex; (2) limited by the Gaussian assumption under strong inhomogeneous recirculation	,
Lagrangian (e.g., CALPUFF, HYSPLIT, TAPM)	(1) handles nonstationarity and spatial heterogeneity; (2) suitable for mid to long-range and complex meteorology (e.g., sea–land breeze); (3) mature in regulatory applications	(1) cost grows with N; (2) limited for strong near-field recirculation; (3) parameterization differences add uncertainty	−
CFD–RANS (k–ε/k–ω)	(1) more accurate for complex terrain/building flows; (2) steady or quasi-steady flow fields; (3) engineering-robust with manageable cost	(1) averaging loses transients; (2) sensitive to mesh setup; (3) not ideal for real-time inversion	,
CFD–LES	(1) high accuracy; (2) resolves transient details; (3) captures vortices and unsteady dispersion; (4) suited to complex disturbed environments	(1) high compute and storage; (2) needs time-resolved fields for adjoint/backward runs; (3) sensitive to mesh and time step	,

In the current understanding, the use of large eddy simulation (LES) for solving the adjoint equation remains primarily confined to research studies and is considered difficult to apply in engineering practice. When LES is employed to compute the inverse time-stepping and dispersion processes, it requires storing a time-series flow field and concentration data for the entire monitoring domain. Given the small time steps and high-resolution grids demanded by LES, even when computational load is reduced through the source–receptor approach, the resulting data volume remains prohibitively large for practical applications. In recent years, techniques for compressing turbulent flow data have advanced rapidly. For instance, wavelet-based compression methods can now reduce data size by up to 2 orders of magnitude while maintaining accuracy. , Meanwhile, the dynamic mode decomposition (DMD) method, grounded in dynamical systems theory, can extract the spatiotemporal structures of gas flow and offers strong capabilities in reconstructing and predicting flow states. Zhu et al. applied the DMD method to achieve STE in unsteady flow fields, maintaining high accuracy while significantly improving computational efficiency.

Compared with traditional numerical simulations, data-driven approaches (particularly deep learning) learn the input–output mappings directly, enabling faster predictions and avoiding computationally intensive iterations. Essentially, such models act as surrogate representations of dispersion physics, similar to data compression methods, both aiming to reduce the high-frequency computational cost of forward models. However, their accuracy is strongly dependent on the quality and physical representativeness of the training data. Alaoui et al. enhanced the accuracy of dispersion models and STEs by integrating random forest algorithms with traditional Gaussian plume models and automatically identifying atmospheric stability categories. Ma et al. , proposed a machine learning algorithm (MLA model) that serves as a dispersion model with high predictive accuracy and efficiency and combined it with the Markov Chain Monte Carlo (MCMC) method to estimate source terms (Figure a). The superiority of this approach was validated through the Prairie Grass field experiment. Wang et al. coupled artificial neural networks (ANNs) with gas dispersion models in the PHAST software to construct a surrogate model for rapid prediction of the spatiotemporal distribution of released gas concentrations, validated via case studies. Destero et al. addressed the challenge of processing large-scale data sets by implementing GPU-based deep recurrent neural networks (RNNs), achieving fast and accurate simulations of gas dispersion accident scenarios. Travis et al. developed a forward dispersion surrogate model for STE using LES data sets combined with ANN architectures (Figure c). The Rocky Mountain Oilfield Testing Center (RMOTC) experiment demonstrated that this method achieved a high-throughput performance with an error margin of only 11%.

5.

Application of data-driven intelligent agent model to STE algorithm: including: (a) MLA model as dispersion model, combined with MCMC method to estimate source terms. Reprinted with permission from ref . Copyright 2021 SPRINGER. (b) Train ANN schematic diagram through LES numerical simulation data. (c) Schematic diagram of RMOTC experiment, including one or more storage tanks, wellhead, and separator, with a total of 4 sensors placed. Reprinted with permission from ref . Copyright 2020 Elsevier.

In summary, the dispersion of gases in the atmospheric environment is fundamentally a fluid dynamic process. The Gaussian model, as a classical analytical solution derived from the convection–dispersion equation, offers simplicity and computational efficiency. However, its accuracy diminishes under low-wind-speed or near-field dispersion conditions. CFD models, grounded in the principles of fluid mechanics, can accurately simulate pollutant dispersion by constructing physical models that replicate real environmental conditions. While CFD provides higher precision in small-scale methane dispersion simulations, its computational cost is substantial due to the large number of differential equations involved. Consequently, few studies directly employ CFD models for STE, as their solution times are too long for real-time inversion. It should be emphasized that the purpose of this study is to obtain source-term information by minimizing the concentration-based cost function through forward modeling. The computational expense of CFD models renders them unsuitable for achieving real-time inversion of the source parameters. Building data-driven surrogate models trained on experimental or CFD-generated data sets may provide an effective means to balance computational efficiency and accuracy. Rapid prediction of methane dispersion behavior is not only a crucial step in STE but also plays an important role in reducing property losses, ensuring operational safety, and supporting environmental compliance for industrial facilities.

Estimation Algorithms

According to the characteristics of oil and gas industry facilities and the number of point sources to be estimated, emissions in practical inversion processes can be categorized into single-point source inversion and multipoint source inversion. Subsequent analyses in this study differentiate between these two cases. In the oil and gas industry, many studies use a single effective point source to characterize emissions at the site scale, especially when the geometric relationship between observation footprints and source receptors is insufficient to support more detailed attribution. Well sites, pressure-regulating and -metering stations, gas stations, and flare facilities are often considered as overall emission sources. When the source position is assumed to be known and only the source intensity is unknown, the forward diffusion model usually shows a linear relationship with the source intensity, which facilitates the quantitative inversion of emission rates. Most snapshot measurement studies have adopted this solution framework. − In contrast, multipoint source scenarios feature multiple processes and complex emission patterns. Examples of such scenarios include natural gas processing plants, gathering stations, and offshore production platforms. Since these emission sources cannot be merged or treated collectively, it is necessary to apply STE algorithms to trace, identify, and quantify each individual emission source.

Research on STE algorithms primarily encompasses two components: cost functions and estimation algorithms. Studies of cost functions focus on optimizing the STE process to enhance computational efficiency and estimation accuracy. For example, Sharan et al. proposed a least-squares-based data assimilation technique that reduces the degrees of freedom of the unknown parameters by expressing source intensity as a function of its spatial position, thereby decreasing computation time. Wang et al. employed the statistical Nemenyi test to assess the performance of 11 composite cost functions across 68 STE tasks based on grassland field experiments, analyzing the relationship between composite cost functions and multiobjective optimization. Their results indicated that a newly proposed composite cost function exhibited superior performance in estimating both source location and emission rate. Efthimiou et al. , and Kovalets et al. adopted the Pearson correlation coefficient as the cost function to infer source coordinates, calculated source intensity using the least-squares method, and validated their two-step separation cost function through wind tunnel experiments simulating atmospheric flow and tracer dispersion. This method does not require prior knowledge of the source location and significantly improves both the accuracy and computational speed of STE.

Deep learning-based STE algorithms are rapidly emerging. − However, more mature and generalizable approaches remain the mainstream approach in STE research. These include optimization algorithms and Bayesian methods grounded in probabilistic inference. Regardless of the specific methodology, the overall conceptual framework is largely consistent. First, an initial estimate of the emission source intensity is assigned within a defined range, and a dispersion model is used to predict the concentration at each monitoring point. Then, by construction of a cost or likelihood function, the optimal source parameters are obtained through iterative updates. This process ultimately yields estimates of the source location and intensity.

Optimization Algorithm

The purpose of optimization methods is to identify the minimum value of the cost function, which is formulated based on the calculated and observed concentrations. By assuming that the parameter combination yielding the smallest difference represents the optimal estimate of the source term, we can take various forms. The most fundamental form is the sum of the squared differences between the observed concentration and the simulated concentration.

$$J=\sum _{i=1}^{n_{\mathrm{obs}}}{(C_i^0-C_i^S)}^2$$ 4

Most optimization techniques employ an iterative process, applying different update rules to minimize the objective function and generate progressively improved parameter estimates. A wide variety of algorithms have been developed to solve the minimization problems associated with cost functions, including gradient-based algorithms, particle swarm optimization (PSO), simulated annealing (SA), and genetic algorithms (GA). Table presents a comparative analysis of the characteristics of these optimization algorithms.

4. Comparative Analysis of the Characteristics of Optimization Algorithms.

method	core idea/update mechanism	advantages	limitations/risks	ref
gradient-based (least-squares, BFGS, etc.)	iteratively update parameters using the objective’s gradient or a quasi-Newton approximation to minimize residuals	low computational cost; fast convergence; suitable for real-/near-real-time applications	partial derivatives hard to express in high dimensions; prone to local minima; sensitive to initial values; no direct uncertainty estimates	,
simulated annealing (SA)	stochastic global search via an “annealing” process; accepting worse solutions with a probability helps escape local minima	weak dependence on initials; strong global exploration; robust to nonconvex objectives	slower convergence; schedule/temperature need tuning; no direct confidence intervals
genetic algorithm (GA)	population-based search with selection–crossover–mutation toward a global optimum	suited to nonconvex, discrete and combinatorial spaces; searches many parameters jointly	time-consuming; premature convergence possible; needs tuning (population size, mutation rate); no direct uncertainty	,
particle swarm optimization (PSO)	swarm particles update velocity and position to explore a continuous parameter space	gradient-free; simple to implement; few hyper-parameters; good for continuous variables	may stagnate in local optima; sensitive to inertia weight and acceleration factors; efficiency drops in high-dimensional or highly multimodal cases; no direct uncertainty	,

Single optimization algorithms often suffer from drawbacks such as overfitting risk and high sensitivity to initial parameter values when solving STE problems. To address these limitations, recent research has increasingly focused on hybrid optimization strategies that combine the strengths of multiple algorithms. These approaches typically employ global algorithms to quickly identify promising solution regions, followed by local algorithms for fine-tuning, resulting in a higher convergence efficiency and improved overall performance.

Li and Zhang combined a Parallel Genetic Algorithm (PGA) with the Nelder–Mead (NM) simplex method, initializing the simplex using the final population from the PGA and refining the best vertex through the NM search. The results demonstrated that this hybrid approach significantly enhanced the computational efficiency and stability. Cui et al. proposed a combined PSO-NM and validated it through 68 SO₂ leakage experiments. They also introduced a comprehensive estimation framework to analyze the influence of atmospheric conditions on algorithmic performance, showing that estimation accuracy and robustness were highest under atmospheric stability classes E and C. Wang et al. developed a hybrid algorithm integrating PSO, GA, and SA. Experimental results indicated that this hybrid approach substantially improved both convergence efficiency and computational accuracy compared with single-algorithm implementations. Kendler et al. evaluated STE using a combination of hyper-heuristic SA and an adaptive multiobjective evolutionary algorithm (MOEA). The method’s effectiveness was verified through model case studies, and two complementary measures were proposed to assess the complexity of STE under sparse sensor data conditions. Jang et al. analyzed the performance of three gradient-free optimization algorithms for STE and proposed strategies to enhance inversion performance, such as incorporating prior information, applying uncertainty-reduction techniques, and optimizing observation locations. Their findings showed that the ensemble Kalman inversion (EKI) achieved superior accuracy and computational speed compared with PSO and GA. Overall, hybrid optimization algorithms combine the global search capabilities of metaheuristic methods with the local refinement ability of classical optimization techniques. Compared with single optimization algorithms, hybrid approaches exhibit greater efficiency, yield more accurate estimates, and reduce dependence on the initial parameter settings.

In existing research, most STE algorithms focus on solving single-point source problems, while fewer studies address multipoint source inversion. However, multisource emissions are more frequent and practically significant in real-world oil and gas operations. Compared with single-source estimation, multipoint source assessment faces three core challenges. First, the unknown number of emission sources increases the dimensionality of the parameter space and complicates the inversion process. Second, sparse sensor networks often record signals that are the result of the superposition of multiple dispersion plumes. This makes it difficult to isolate the contribution of individual sources and results in mathematical ill-posedness. Under certain meteorological conditions, source identification is further complicated by severe collinearity interference. This occurs, for example, when multiple plumes converge at a single sensor node due to wind fields. Finally, near-field weak sources and far-field strong sources may produce indistinguishable concentration responses. Such parameter identifiability issues significantly reduce the uniqueness and robustness of inversion results.

Under an optimization framework, Lulshi and Stockie estimated the emission intensities of four point sources with known locations using measurement and meteorological data, employing a least-squares approach. Singh et al. used a weighted least-squares inversion algorithm to estimate two or three known point sources and provided a sensitivity analysis comparing the weighted and unweighted approaches. These studies assume that the number of sources is known, an assumption that is rarely satisfied in practice. Estimating the number of sources markedly increases the computational time for STE. Annunzio et al. determined both the number and the locations of multiple instantaneous and steady-state sources in the FFT-07 field experiment by introducing the multiple-field estimation method (MEFA). They further showed that source-to-source spacing affects inversion accuracy: when sources are too close, individual contributions become indistinguishable. Wang et al. combined principal component analysis (PCA) with a modified genetic algorithm (MGA) to invert multisource terms; PCA was first used to infer the number of sources and candidate regions, after which MGA retrieved source locations and intensities. Numerical simulations indicated that, while effective for typical source distributions, identification accuracy degrades under certain conditions (e.g., large downwind distances combined with small intersource spacing). Albani and Albani integrated finite-element formulations, least-squares estimation, and high-fidelity meteorological modeling within a Tikhonov-type regularized composite cost function; using a recursive Gauss–Seidel solver, they estimated multiple source locations and strengths while accounting for data noise and uncertainty. Wang et al. modified a two-step optimization scheme by maximizing the Pearson correlation coefficient to identify new source locations at each iteration and by estimating source strengths via least-squares minimization of residuals without prior initialization; the method was validated with the European Tracer Experiment (ETEX).

Bayesian Inference

The Bayesian-based source-term information estimation method utilizes a probabilistic framework to formulate inversion problems, effectively addressing uncertainties in the observed data and models. This approach parametrizes the source term as a multidimensional random variable and employs random sampling methods to derive the posterior probability density function of the parameters. The maximum probability estimate of the posterior distribution is considered to be the true value of the source parameter. The formula is expressed as follows:

$$P(\theta |D)=\frac{P(D|\theta )P(\theta )}{P(D)}$$ 5

where P(θ|D) represents the probability of estimating the source parameter θ given the known observation data D, P(D) is the marginal probability, usually a normalization constant. P(θ) is the prior probability, representing the probability of the source parameter θ before any observations are made. During the source-term inversion process, common prior probability distributions include the uniform distribution, Gaussian distribution, and Jeffreys prior distribution. P(D|θ) is the likelihood function, which represents the probability of observing a concentration D given the source term θ. It quantifies the difference between the simulated and the observed concentration. The most common likelihood probability is a normal distribution. Additionally, other distributions such as the logarithmic normal distribution and the Poisson–Bernoulli distribution can also be used, depending on the noise error assumptions in measurements and forward models. When a normal distribution is used, the likelihood function can be expressed as

$$P(D|\theta )\propto \exp [-\frac{1}{2}\sum _{i=1}^m\frac{{(D_i-R_i)}^2}{{\sigma }_d^2+{\sigma }_m^2}]$$ 6

where D _i represents the measured concentration at the ith sensor, while R _i is the simulated concentration at the ith sensor, calculated using the dispersion model. σ _d and σ _m denote the measurement and modeling variances of the sensors, respectively. These variances can typically be determined as a ratio of the measured concentrations.

Due to the complex mathematical form of , obtaining an analytical solution directly is challenging. The Monte Carlo (MC) sampling method is commonly employed to determine the posterior distribution of source parameters; however, its computational efficiency is low, particularly when numerous source parameters are involved. Consequently, more advanced and practical approaches, such as MCMC, Sequential Monte Carlo (SMC), Approximate Bayesian Computation (ABC), and Differential Evolution Monte Carlo (DEMC) have been developed. These methods enhance the efficiency and accuracy of Bayesian inference sampling from different perspectives, enabling a more robust STE under sensor noise conditions. Table provides a comparative analysis of the characteristics of these sampling methods.

5. Comparative Analysis of the Characteristics of Different Sampling Methods.

method	advantages	limitations	representative findings/references
MCMC	applicable to nonconvex and high-dimensional posteriors; can provide uncertainty estimates and identify multiple modes	repeated calls to the forward model lead to high computational cost; mixing and convergence depend on tuning and initial values	modeling and reconstructing dispersion parameters for zero/nonzero readings near detection limits to improve estimation accuracy
			constructing likelihoods based on source–receptor relationships and validating localization and quantification in two field experiments
			using annealing to improve the mixing rate of Markov chains and accelerate convergence
			combining meteorological and dispersion uncertainty to address intermittent readings from low-cost sensors
			high-resolution Lagrangian model plus MCMC validated in realistic urban experiments
			CFD combined with MCMC improves source localization and quantifies source strength under sparse sensors
			introducing adjustable regularization parameters to effectively identify intermittent emissions
SMC	supports online/real-time updating; parallel friendly; robust for non-Gaussian and nonlinear systems	particle degeneracy and loss of diversity; performance is sensitive to weight and resampling strategies	sequential correction plus SMC inversion of source strength and position, robust on synthetic data with multiple sensor configurations
			for 5-dimensional parameter estimation, SMC gives better source location information than MCMC, but source strength estimates are limited by forward-model error
			mobile binary observations with SMC are effective in three wind condition experiments
			SMC with sensor collaboration (infotaxis) improves source-search efficiency
			recycling horizon infotaxis (RHI) and random sampling enhance the success rate of gradient-free SMC search strategies
ABC	suitable for unknown noise or threshold observations; adaptable to complex likelihood structures	accuracy depends on the choice of distance measure and tolerance; computational cost can still be high	adaptive multimodel ABC improves acceptance rate and is suitable for obstacle-rich scenarios
			ABC replacing the SMC likelihood is applicable for reconstructing 7-dimensional parameter estimation in OLAD experiments
			adaptive tolerance sequences, optimal perturbation kernels and resampling improve ABC performance, with cross-stability robustness evaluated using Nemenyi tests
DEMC	faster mixing and convergence than traditional MCMC; more robust for multipeak and strongly correlated posteriors	still requires many forward-model calls; covariance and step-size choices affect performance	intermittent source inference for emergency response using historical model outputs for evolutionary updates
			provides reasonable reservoir-parameter estimates even under high-noise (up to 25%) observations
			DEMC with convection-diffusion models performs better than GA for identifying and predicting continuous sources in rivers
			compared with traditional MCMC, DEMC achieves better convergence and accuracy in highly nonlinear and multimodal systems

The MCMC method is the most widely used Bayesian sampling technique in the field of STE. Its core strength lies in its strong generality: it can effectively handle nonconvex, high-dimensional posterior distributions while providing comprehensive uncertainty quantification. However, it also has clear limitations, including high computational costs and convergence that depends heavily on parameter tuning, which has driven the development of subsequent algorithms. The SMC and ABC were developed to overcome some of the shortcomings of MCMC. SMC addresses online and real-time problems through its parallel particle sampling and resampling mechanism. Its sequential updating feature allows it to process time-series data and perform dynamic state estimation. The ABC method tackles the challenge of constructing likelihood functions. For complex observation processes and unknown noise models, ABC provides a practical probabilistic inference framework by replacing explicit likelihoods with distance metrics. , More recently, the DEMC has been introduced to further enhance the core performance of MCMC. By integrating the global search capability of differential evolution with MCMC’s sampling principles, DEMC achieves multichain parallelism and adaptive proposal mechanisms, significantly improving convergence speed and exploration efficiency for complex posterior distributions, such as multimodal or strongly correlated cases. In summary, there is no universally optimal algorithm, and the practical choice depends on the specific application scenario. Future research is expected to focus on how to intelligently select, combine, or even adaptively switch among these algorithms based on engineering constraints and problem complexity, thereby achieving an optimal balance between inversion accuracy, computational efficiency, and result robustness.

For multisource traceability scenarios, Yee proposed a reversible-jump Markov Chain Monte Carlo (RJMCMC) algorithm that allows Markov chains to transition between models of different dimensions. By adding or removing existing sources and incorporating Lagrangian stochastic models along with source-receptor relationships, this method enables the estimation of unknown multipoint emission sources. However, the computational efficiency of this algorithm remains relatively low. Wade and Senocak combined Bayesian inference with a comprehensive scoring framework that evaluates three metricserror (scatter), bias, and correlation componentsto determine the number of emission sources. In their approach, turbulent diffusion parameters were treated as unknown variables, transforming the system into a data-driven model and improving the overall accuracy of the STE. Nguyen et al. considered sensor measurement uncertainty and developed a multisource-localization algorithm based on SMC. This method employs an adaptive resampling strategy using effective sample size (ESS), which automatically determines the number of iterations required, thereby enhancing computational speed and accuracy. Albani et al. integrated finite-element formulations with multivariate dynamic models to construct a wind-field representation. Using a combination of the PSO method and an adaptive MCMC algorithm, they successfully identified multiple atmospheric emission sources. This approach improved the computational performance of the STE by embedding more physical information into the Bayesian inference process. Although these algorithms demonstrate substantial improvements over traditional methods, most remain constrained by prior information and computational cost. In cases involving numerous emission sources, the dimensionality of the parameter space expands dramatically, resulting in sharply increased computational burdens. These limitations hinder their application in real-time STE for automated monitoring systems.

Comparison and Analysis

This section differentiates between single-point and multipoint source scenarios based on the characteristics of oil and gas industry facilities and introduces both optimization and Bayesian inference STE methods. In optimization-based approaches, point estimates of source parameters are obtained by minimizing the cost function between measured and model-predicted concentrations. Although hybrid optimization algorithms enhance accuracy compared with single algorithms by integrating global and local search strategies, they still face challenges, such as the risk of becoming trapped in local optima when handling high-dimensional parameter spaces. Moreover, these methods cannot systematically incorporate prior information or provide uncertainty quantification for their estimation results.

In contrast, Bayesian-inference-based methods provide a probabilistic framework capable of integrating prior knowledge into the estimation process. This feature is particularly valuable in monitoring scenarios at oil and gas field facilities where data are sparse as well-constructed prior distributions can effectively compensate for limited observational information. These methods output the posterior probability distribution of the parameters, enabling uncertainty quantification of the estimation results, for example, through confidence intervals, which is essential for comprehensive risk assessment. Although the computational cost of Bayesian approaches is generally higher than that of optimization-based methods, recent advances in sampling techniques, such as SMC and DEMC, have significantly improved their computational efficiency. Table provides a systematic summary of optimization algorithms and Bayesian inference methods.

6. Systematic Comparison of Optimization-Based and Bayesian Inference Methods.

aspect	optimization-based methods	Bayesian inference methods
output	single best solution	posterior distribution of parameters
uncertainty	no; intervals not provided directly	yes; main strength, yields credible or confidence intervals
prior information	hard to include; usually via regularization terms	natural to include through prior distributions
computational efficiency	relatively high, especially for gradient-based methods	usually lower; many samples and substantial computation required
sensitivity to initialization	high (notably local optimizers)	lower with well-designed samplers and sufficient burn-in
suitability for multiple sources	performance degrades as dimension grows; prone to local optima	flexible in principle, but computational cost rises steeply with the number of sources
typical use cases	fast solutions when uncertainty quantification is not critical	risk assessment, quantified uncertainty, and sparse data problems where priors provide important information

Summary

This section systematically examines the modeling and inference processes, dispersion models, and estimation algorithms that constitute the STE technology framework. The dispersion model describes the physical process of pollutant dispersion, while the estimation algorithm serves as the core mechanism for inverting source parameters from sparse observational data. However, the successful implementation of an STE system requires more than simply combining these two components; it demands a careful alignment between the model and the algorithm tailored to the specific characteristics of the problem. Table provides a systematic summary of representative STE research studies published in recent years.

7. Recent Studies on STE Algorithms.

ref	dispersion model	sensor deployment	source	algorithm	source parameters
	Gaussian plume model	equidistant arc	single	GA–PS	x, y, z, Q
	CFD–RANS	array	single	gradient	x, y, z, Q
	Gaussian plume model	equidistant	single	PGA–NM	x, y, z, Q
	Gaussian plume model	equidistant arc	single	PSO–NM	x, y, z, L, Q
	BPNN	equidistant arc	single	PSO + GA + SA	x, y, Q, U, Dir
	GAPDM	equidistant/random	single/multiple	SA–MOEA	x, y, Q
	Gaussian plume model	random	single/multiple	EKI/PSO/GA	x, y, z, Q
	GRAMM–GRAL	random	single	MCMC	x, y, z, Q, t
	CFD–RANS	random	single	MCMC	x, y, z, Q, t
	Lagrange statistic	moving binary	single	SMC	x, y, Q, t
	SCIPUFF	random	single	ABC	x, y, d, v, Q, t s , t d
	CFD–LES	array	single	MCMC	x, y, Q
	Eulerian dispersion model	array	single/multiple	DEMC	x, y, Q
	Gaussian plume model	array	single/multiple	PCA–MGA	x, y, Q
	CFD	array	multiple	Gauss-Seidel-like algorithm	x, y, z, Q
	signal attenuation model	random	multiple	SMC	x, y, Q
	CFD	array	multiple	MCMC–PSO	x, y, z, Q

The analysis reveals a clear trade-off between model complexity and algorithm selection in existing research. Computationally lightweight Gaussian models are often paired with computationally intensive but highly exploratory hybrid optimization algorithms (such as PGA-NM and PSO-NM) or advanced Bayesian methods, since the rapid estimation of forward models allows these algorithms to perform a greater number of iterative searches. In contrast, computationally demanding CFD models are typically coupled with algorithms that have controlled iteration counts, such as MCMC, to ensure that inversion can be completed within a feasible time frame. The complexity of the problem, particularly the transition from single-point to multipoint source estimation, serves as a key driver of algorithmic innovation. As shown in the table, researchers have developed more sophisticated strategies for addressing multisource challenges, such as incorporating PCA-assisted genetic algorithms or designing hybrid Bayesian optimization frameworks to overcome difficulties associated with unknown source quantities and signal superposition.

Summarizing existing STE algorithms, it is evident that most studies have been conducted under idealized scenarios or numerical experiments, which primarily establish the theoretical upper limits of algorithmic performance. However, in real-world engineering applications, deviations from these ideal assumptions often lead to substantial declines in accuracy and robustness, making the transition from theory to practice a central research challenge in recent years. For example, the unknown number of emission sources greatly increases the difficulty of source parameter inversion, which is a condition commonly encountered in field measurements. Attempting to exhaustively solve for all possible combinations of source parameters results in an exponential increase in the computational cost. Consequently, existing methods generally estimate the number of sources that best fit the observed data and then determine the corresponding source positions and intensities under this constraint. Nonetheless, the dimensional mismatch between the limited number of sensors and the degrees of freedom of source parameters remains the core bottleneck restricting the practical implementation of these algorithms in engineering environments.

Conclusions

This review presents a systematic and comprehensive framework for evaluating methane source terms using a fixed continuous monitoring system. The performance of an STE system depends on the synergistic interaction between front-end data acquisition and back-end modeling. The information gathered by the front-end sensor network constrains the theoretical accuracy achievable in the inversion process, while the performance of the back-end dispersion model and estimation algorithm determines the degree to which this theoretical accuracy can be realized under the given data conditions. Accordingly, this study reviews advances in sensor technology, sensor-deployment optimization, dispersion modeling, and estimation algorithms to identify the key technical bottlenecks that limit the effectiveness of current monitoring systems and propose strategies for improving the accuracy of methane emission quantification. The main conclusions of this work are as follows:

At the data acquisition stage, there remains a disconnect between the existing sensor-deployment strategies and inversion objectives. This study identified three main criteria for optimizing sensor placement. The geometry-based criterion emphasizes spatial coverage integrity, ensuring that the monitoring network captures emissions across the entire target area. The quantity optimization criterion prioritizes the cost-effectiveness of the sensor network architecture and is particularly applicable to the upgrading or reconstruction of existing monitoring systems. Meanwhile, the information entropy criterion quantifies the informational contribution of each newly added sensor, aiming to maximize the total information gained from a limited number of sensors. Most existing strategies prioritize event detection probability, which helps ensure coverage but often neglects direct coupling to the goal of minimizing parameter uncertainty in subsequent inversion. This detection-driven design, therefore, remains a fundamental bottleneck for accurate quantification.

At the modeling and estimation stage, this study identifies a trade-off among accuracy, computational efficiency, and complexity in selecting models and algorithms. The analysis indicates that (1) data-driven surrogate models and turbulence data compression can bridge the gap between high-fidelity CFD and lightweight Gaussian formulations; (2) Gaussian models are well-suited for integration with computationally intensive global optimization and Bayesian inference, whereas CFD models should be paired with algorithms that have controllable iteration budgets; and (3) compared with single-point estimates, Bayesian frameworks can incorporate prior information to mitigate data sparsity and provide principled uncertainty quantification.

Future Perspectives

Based on the technical bottlenecks revealed by the above conclusions, future research in this field should prioritize the following directions:

• (1)Developing sensor-deployment optimization theory for inversion accuracy: Future optimization criteria must evolve from a single detection coverage to a multicriteria optimization framework centered on information theory and detection coverage. This deployment strategy directly linked to inversion accuracy is the key to enhancing the value of data information from the source.
• (2)Developing high-fidelity proxy models that balance efficiency and accuracy: To address the inherent contradiction between fidelity and computational efficiency in dispersion models, developing efficient proxy models is a key research direction. Future research should focus on two directions: first, using machine learning methods to construct robust data-driven proxy models, learning and reproducing the input and output relationships of high-cost CFD simulations; Second, effective compression techniques for high-dimensional turbulent data, such as principal component analysis (PCA) or orthogonal decomposition (POD), should be studied to significantly reduce the required data dimensionality and computational overhead.
• (3)Overcoming the difficulty of probabilistic inversion under multisource sparse data: Single-source inversion technology has become relatively mature, but inversion under multisource and sparse data is still the core bottleneck. Future algorithm research should focus on Bayesian frameworks, advanced sampling techniques that can handle problems with unknown source quantities, and combined with compressive sensing theory to fundamentally solve the solvability of such severe pathological inverse problems.

• (4) Benchmarking and verification for real industrial scenarios: Currently, the performance estimation of most STE algorithms relies on idealized numerical simulations, which limits their translation into engineering practice. To bridge the gap between theory and application, future research needs to move from idealized numerical simulations to real industrial scenarios, systematically considering the impact of nonideal factors, such as complex terrain, dynamic background concentration, sensor failures, etc. on the entire continuous monitoring system technical framework, establishing standardized testing benchmarks and data sets to verify and compare the real performance of different technical solutions.

No data sets were generated or analyzed during the current study.

Z.X.: Conceptalization, data curation, fommal analysis, investigation, methodology, visualization, writingoriginal draft, and writingreview and editing. J.T. (Corresponding Author): Supervision, investigation, funding acquisition, and writingreview and editing. R.L.: Data curation, resources, investigation, and writingreview and editing. G.T.: Data curation, resources, investigation, and writingreview and editing. Y.Z.: Data curation, investigation, and visualization. M.S.: Data curation, investigation, and visualization. R.M.: Writingreview and editing and investigation.

This study has been supported from the Shandong Provincial Key Laboratory of Oil, Gas and New Energy Storage and Transportation Safety.

The authors declare no competing financial interest.