A Review of City-Scale Methane Flux Inversion Based on Top-Down Methods

Highlights

What are the main findings?

• Top-down inversion studies at the city-scale reveal substantial discrepancies with bottom-up emission inventories, with posterior uncertainties typically ranging between 11% and 28%.
• Bayesian and hybrid (variational-ensemble Kalman) approaches demonstrate notable advantages: the former can effectively address issues of posterior uncertainty, while the latter strikes a balance between accuracy and computational efficiency.

What is the implication of the main finding?

• The observed inconsistencies underscore the necessity of advancing city-scale methane quantification methodologies to ensure robust and policy-relevant emission assessments.
• A comprehensive framework combining high-resolution inventories, coordinated observations, AI-enhanced modeling, and isotopic analysis can significantly advance the reliability of methane emission monitoring and support more effective climate policies at the city-scale.Second bullet.

Abstract

As urbanization intensifies, the quantification of methane (CH₄) emissions at city scales faces unprecedented challenges due to spatial heterogeneities from industrial and transportation activities and land use changes. This paper provides a review of the current state of top-down atmospheric CH₄ emission inversion at the city scale, with a focus on CH₄ emission inventories, CH₄ observations, atmospheric transport models, and data assimilation methods. The Bayesian method excels in capturing spatial variability and managing posterior uncertainty at the kilometer-scale resolution, while the hybrid method of variational and ensemble Kalman approaches has the potential to balance computational efficiency in complex urban environments. This review highlights the significant discrepancy between top-down inversion results and bottom-up inventory estimates at the city scale, with inversion uncertainties ranging from 11% to 28%. This indicates the need for further efforts in CH₄ inversion at the city level. A framework is proposed to fundamentally shape city-scale CH₄ emission inversion by four synergistic advancements: developing high-resolution prior emission inventories at the city scale, acquiring observational data through coordinated satellite–ground systems, enhancing computational efficiency using artificial intelligence techniques, and applying isotopic analysis to distinguish CH₄ sources.

1. Introduction

The accumulation of greenhouse gases emitted into the atmosphere as a results of human activities has resulted in a 1.1 °C rise in the Earth’s surface temperature since 1850 [1]. A further temperature increase may result in irreversible changes in the Earth system, such as coral reef die-offs, permafrost thawing, and the disappearance of mountain glaciers [2]. Greenhouse gases include water vapor (H₂O), nitrous oxide (N₂O), carbon dioxide (CO₂) and methane (CH₄). H₂O is the strongest GHG but is usually not considered because of its short atmospheric lifetime (less than 2 weeks) as compared to 9 years for CH₄ and 100 years for CO₂. The concentrations of N₂O are much smaller than those of CO₂ and CH₄. CH₄ is a potent greenhouse gas with a much larger global warming potential (GWP) than CO₂ on a per-mass basis [3,4]. Since the start of industrialization, atmospheric CH₄ concentrations have more than doubled, contributing approximately 20% to current human-induced global warming [5]. Compared to CO₂, CH₄ has a higher warming potential but a shorter atmospheric lifetime, making CH₄ emission reductions likely to have significant short-term impacts on global warming [6]. Global Methane Assessment shows that reducing CH₄ emissions by 40–45% by 2030 would avoid nearly 0.3 °C of global warming by 2045 (UNFCC; https://unfccc.int/news/global-assessment-urgent-steps-must-be-taken-to-reduce-methane-emissions-this-decade, last visit 16 July 2025). In November 2021, 105 countries endorsed the “Global Methane Pledge”. This pledge is intended to limit global warming to under 2 °C above pre-industrial levels. The U.S. National Academies’ Earth Science Decadal Survey (2017–2027) identified “CO₂ and CH₄ fluxes and trends, with quantification of point sources and identification of sources and sinks” as one of the top observational priorities [7]. Quantifying CH₄ emissions is pressing and must be addressed urgently. The two main methods used to determine CH₄ emissions are the bottom-up (BU) and top-down (TD) approaches. Bottom-up methods calculate the sum of the contributions from different anthropogenic sources (fossil fuels, waste management, etc.), using activity data and emission factors for each type of activity, and calculate emissions from natural sources (wetlands, termites, etc.) using biogeochemical models [8]. Bottom-up methods provide detailed estimates of emission from specific CH₄ sources. However, discrepancies often arise when comparing total emissions with observations [9]. These inconsistencies may stem from inaccuracies regarding emission factors and activity data [10], or from poor performance of process models [9].

Atmospheric CH₄ observations, combined with atmospheric transport models and data assimilation methods, inform large-scale assessments of CH₄ sources and sinks [11]. These methods, commonly known as “inversions” or top-down accounting, quantify CH₄ flux by incorporating CH₄ measurements from towers, aircraft, or satellites [12]. An advantage of top-down methods is that they rely on observational data and atmospheric transport models to invert fluxes, enabling a more accurate and objective representation of actual emissions [11,13]. Another advantage is that emissions, on a large scale, are available from top-down methods within a short time (months), whereas, bottom-up estimates require a long time to estimate the number of sources and their emission factors, and updates typically require a few years. Top-down approaches infer the spatial distribution of total emission fluxes based on atmospheric observations. However, due to the diversity of CH₄ sources and the overlapping atmospheric dispersion of emissions from different origins, the resulting signals are superimposed, making it difficult to directly attribute emissions to specific sources or sectors [14].

Numerous studies [15,16,17] have applied top-down approaches to estimate CH₄ fluxes at global and regional scales. For the city scale, however, the coarse spatial resolution used in these studies makes it difficult to accurately quantify CH₄ fluxes using top-down inversion methods. Several studies have reported that top-down inversion estimates for certain cities differ substantially from the Emissions Database for Global Atmospheric Research (EDGAR) greenhouse gas emission inventory [18,19,20,21]. Top-down CH₄ flux inversion at the city scale faces several challenges: the lack of detailed city-scale CH₄ emission inventories, inaccuracies in wind field simulations, sparse observational data, and the inability to distinguish between different emission sources.

The term “city scale” in this paper refers to the entire administrative boundary of a city, encompassing the urban core, suburban areas, and rural regions within its jurisdiction. This study focuses on the current state of top-down CH₄ flux inversion at the city scale. Top-down inversion methods for CH₄ fluxes will be discussed in Section 2, including emission inventories, observations of CH₄ concentrations, transport models and inversion methods. An overview of inversion results at the city scale will be presented in Section 3, including emission characteristics and associated uncertainties in the inversion outcomes. A future development framework for city-scale CH₄ flux inversion based on coordinated satellite–ground observations is proposed in Section 4.

2. Top-Down Atmospheric Inversion Methods for CH₄

Figure 1 illustrates the overall work logic of the top-down CH₄ flux inversion method. First, the top-down flux inversion algorithm requires the spatial distribution of prior fluxes as the basic input. Usually, global bottom-up carbon emission statistics are transformed into grid-based maps and this information is compiled into an emission inventory. Most studies select prior fluxes based on publicly available gridded emission inventories, which are mostly at the global scale and generally have low spatial resolution. At the city scale, not every city has developed a gridded emission inventory; therefore, global inventories offer a convenient alternative for scientific research. An overview and detailed description of existing global, regional CH₄ emission inventories is provided in Section 2.1, together with suggestions for constructing prior fluxes.

The second important input is the CH₄ concentration, which serves as a key observational constraint within the inversion framework. These concentration data are assimilated to provide observational information and to adjust prior emission estimates, enabling the optimization algorithm to minimize the discrepancy between observed values and those simulated by the atmospheric transport model. CH₄ concentrations can be obtained through satellite observations and ground-based measurements. The current state of development of these two observation methods will be discussed in Section 2.2.

The atmospheric transport model is an essential part of the inversion algorithm. It requires wind field inputs and simulates the transport of atmospheric constituents to establish the source–receptor relationships between emissions and observed concentrations. There are 2 types of models, Eulerian and Lagrangian and the differences will be explained in Section 2.3. The core of inversion is to determine the difference between the simulated and observed concentrations, expressed in the loss function. The loss function is minimized by adjusting the CH₄ fluxes in an iterative process. The thus determined CH₄ flux value for which the loss function is minimal provides the CH₄ emission which best describes the true state. In this process, various methods can be used for the assimilation of the observed CH₄ fluxes, such as Four-Dimensional Variational method (4D-Var), Ensemble Kalman Filter (EnKF), or Bayesian inversion, each of which will be discussed in more detail in Section 2.4.

To accurately capture the spatial distribution characteristics of city CH₄ fluxes, inverse modeling at the city scale requires the use of suitable high-resolution spatial grids. This imposes more stringent demands on prior emission inventories, observational data, atmospheric transport models, and data assimilation methods than for larger scales such as regional or global. A focused discussion on the key technical challenges and appropriate methodologies for city-scale inversion is provided in Section 2.5.

2.1. Emission Datasets for CH₄

CH₄ sources include anthropogenic and natural sources, with anthropogenic sources contributing 60% and natural sources contributing 40% [15]. Agriculture, energy, and waste management are the primary anthropogenic sectors, accounting for 24%, 22%, and 12% of total emissions, respectively [4]. Contributing 33% of total emissions, wetlands are the primary natural source [4]. The most important CH₄ emission inventories are summarized in Figure 2, together with their spatial resolution, the various activity sectors included in each inventory, their spatial resolution and period covered. EDGAR (Emissions Database for Global Atmospheric Research), CEDS (Community Emissions Data System), and GAINS (Greenhouse Gas–Air Pollution Interactions and Synergies) are the three most representative datasets. They are widely used in global carbon budget assessments, atmospheric chemistry modeling, and policy scenario simulations. These inventories are all based on the IPCC-recommended methodology of “activity data (AD) and emission factors” and share similar top-level classifications for anthropogenic CH₄ sources, including agriculture, energy, buildings, transportation, industrial combustion and processes, and waste (with EDGAR further subdividing industrial combustion and processes). However, they differ significantly in terms of data sources, spatial and temporal resolution, methodological approaches, and update frequency, which in turn affects their applicability and regional accuracy [22,23,24].

2.1.1. Anthropogenic Emission Inventory

EDGAR was developed by the Joint Research Centre of the European Commission [22] and covers the period from 1970 to the present, with the latest version released in 2023. EDGAR provides emissions from 226 countries and regions and features strong policy consistency and data transparency. The frequency of EDGAR updates is related to the AD release cycle, which is generally 2–3 years for full updates. However, many EDGAR emission factors rely on default values, and activity data for non-Organisation for Economic Co-operation and Development (non-OECD) countries are associated with considerable uncertainty, potentially resulting in global CH₄ emission estimates with errors of up to ±50% [10].

CEDS employs a modular stitching strategy that integrates and adjusts data from EDGAR, GAINS, FAOSTAT(Food and Agriculture Organization Corporate Statistical Database), and selected official national reports (e.g., UNFCCC) [23]. According to Hoesly et al. [23], the total CH₄ emissions estimated by CEDS for the year 2010 were approximately 94–98% of the corresponding EDGAR v4.2 values for major countries such as China, the United States, and India. This close agreement is primarily due to CEDS’s reliance on EDGAR and FAOSTAT as its main input data sources for CH₄ emissions.

GAINS emission estimates for CH₄ are typically centered on modeling control technologies and mitigation potential [24], rather than providing complete historical emission time series. GAINS emission estimates are available only at 5-year intervals, with spatial resolution of 0.5° × 0.5°. GAINS emission factors are frequently adopted by datasets such as CEDS as a reference for calibration.

Compared to CEDS and GAINS, EDGAR offers higher spatial resolution at 0.1° (while the original resolution of CEDS is 0.5°, pre-2019 data are currently available at 0.1° resolution), which is more suitable for city-scale inversion than the other two global emission inventories.

Although the aforementioned inventories show relatively high consistency at the global scale, significant discrepancies remain in certain regions. For instance, Tan et al. [25] used the GEOS-Chem model to compare CH₄ emissions over China using CEDS and EDGAR v4.3.2, and compared the results with observations from 11 ground-based sites. The simulations driven by CEDS showed the best agreement, with a mean trend bias of approximately −0.3 ppb per year, while EDGAR resulted in a larger positive bias of 2.4 ppb per year. In contrast, satellite-based inversion studies show that both EDGAR and CEDS tend to misrepresent localized high-emission sources in oil- and gas-rich regions such as the Middle East [26]. In order to provide more accurate prior information, many studies have combined national or sector-specific emission inventories with EDGAR. For example, for their study over the United States, Zhang et al. [27] replaced the U.S. portion of the EDGAR inventory with the greenhouse gas emissions inventory (Gridded methane GHGI) provided by the U.S. Environmental Protection Agency (EPA). Compared with EDGAR, the gridded GHGI provides a more accurate spatial distribution of U.S. CH₄ emissions by incorporating detailed state-, county-, and facility-level data, particularly for oil and gas systems, agriculture, and waste sectors. Unlike EDGAR, which allocates emissions largely based on population density, GHGI reflects actual emission hotspots, such as production basins and livestock clusters [28], but the spatial resolution has not been improved (0.1° × 0.1°). However, publicly available gridded emission inventories are still lacking for many countries.

2.1.2. Natural Source Emission Inventory

Natural sources contribute approximately 40% to the total global CH₄ emissions [29]. For natural sources, one of the most commonly used wetland emission inventories is WetCHARTs (Wetland CH₄ and CO₂ Emissions and Removals Time Series). WetCHARTs was developed through collaboration between several research institutions, providing monthly estimates of CH₄ emissions. These estimates are derived from a combination of several terrestrial biosphere models [30].

CH₄ emissions from biomass burning generally use fire emission databases [31]. The main global fire emission inventories include GFED, QFED and GFAS (Global Fire Assimilation System). GFED has a grid resolution of 0.25° × 0.25°, with temporal resolutions available on daily and monthly scales. QFED provides daily averaged emission data with resolutions of 0.1° × 0.1° and 0.25° × 0.3125° [32]. GFAS has provided global biomass burning emission data at a 0.1° grid resolution since 2003. Unlike GFED, which calculates emissions based on fire area, combustion efficiency, vegetation, and soil types, both QFED and GFAS estimate fire emissions using Fire Radiative Power (FRP). Although the CH₄ emissions from biomass burning provide a high-resolution gridded inventory, due to their high randomness and variability, there is considerable uncertainty in a quantitative sense.

Geological seeps, lakes, and termites are relatively minor natural sources of CH₄ emissions. Inventories for these sources are limited and updated infrequently. The CH₄ simulation module in GEOS-Chem incorporates geological seep and lake emission inventories. However, these inventories have not been updated in recent years. Fung_SoilAbs and MeMo v1.0 are two soil uptake inventories used in GEOS-Chem. Fung_SoilAbs provides spatial distributions of soil CH₄ uptake from 2009 to 2015, with a resolution of 4° × 5°. Murguia-Flores et al. [33] developed a process-based CH₄ nutrient model (MeMo) to simulate and quantify global soil uptake of atmospheric CH₄ and provided an uptake dataset with a resolution of 1° × 1°.

Not only the a priori fluxes of CH₄ need to be considered in the top-down inversion, but the atmospheric sink is also an important static dataset for tracking its uptakes. Atmospheric transport models simulate CH₄ loss based on the input distribution of OH concentrations. Based on 14 collected OH fields, Zhao et al. [34] estimated the global average volume-weighted tropospheric OH concentration to range between 8.7 × 10⁵ and 12.8 × 10⁵ mol cm⁻³. Differences in OH simulations among various chemical transport models were attributed to variations in chemical mechanisms, ozone photolysis rates, and modeled concentrations of ozone and carbon monoxide [35]. Zhao et al. [34] also analyzed the vertical distribution of OH across different models. The results show that models such as CMAM, MOCAGE, and SOCOL3 consistently display a continuous decrease in OH concentration from the surface to the upper troposphere, whereas TransCom model shows an initial increase followed by a decrease. Notably, satellite remote sensing has been shown to provide indirect constraints on the spatiotemporal distribution and trends of OH concentrations at regional scales [36]. Typically, OH concentrations and their variations are inferred from the photochemical relationships between OH and satellite-observed trace gases such as HCHO, NO₂, and O₃ [37].

2.2. Observation of CH₄ Concentration

Accurate information on atmospheric CH₄ concentrations is critical for top-down inversion. The different observation methods, such as ground-based and satellite-based measurements, vary in terms of techniques, coverage, temporal continuity, and accuracy.

2.2.1. Ground-Based Observations

Ground-based observations can be categorized into in situ measurements and ground-based remote sensing. Both approaches play crucial roles in CH₄ flux inversions. In situ observations directly measure the concentrations of target gases in the atmosphere using dedicated instruments. Commonly used techniques include Cavity Ring-Down Spectroscopy (CRDS) [38], Gas Chromatography (GC) [39], Mass Spectrometry (MS) [40], and Tunable Diode Laser Absorption Spectroscopy (TDLAS) [41]. Since the 1950s, various organizations have established near-surface concentration stations around the world, gradually forming a global observational network. The GML (Global Monitoring Laboratory) network is one of the most prominent atmospheric observation networks and has expanded its CH₄ sampling network to 88 sites [42]. Most of the sites rely on flask sampling techniques, collecting air samples at monitoring stations, in the field, or during aircraft campaigns. CH₄ concentrations are then analyzed using high-precision GC or MS. In addition, the GML network includes a limited number of tall towers: currently 8 tall towers are operational, providing information at several heights above the surface. The Advanced Global Atmospheric Gases Experiment (AGAGE), supported by NASA, is a global ground-based observation network that has continuously monitored global atmospheric composition since 1978. AGAGE currently includes 19 observation sites, 5 of which measure CH₄. Before August 1993, CH₄ concentrations were analyzed using a modified GAGE HP5880 microprocessor-controlled gas chromatograph After 1993, to improve CH₄ measurements, Carle AGC-211 gas chromatographs were used in addition to the HP5890, which resulted in improved of the measurement accuracy by more than 2 ppb [43]. In 2008, the Integrated Carbon Observation System (ICOS) was established. ICOS supplies observations from nearly 180 stations in 16 European countries. As a major pan-European research infrastructure, ICOS provides high-precision, standardized, long-term greenhouse gas measurements, including CH₄, through its Atmosphere Thematic Centre (ATC). ICOS includes more than 80 measurement stations using CRDS and Fourier-transform infrared spectroscopy (FTIR), which enable CH₄ mole fraction measurements with uncertainties typically below 2 ppb [44].

Ground-based remote sensing techniques primarily provide measurements of column- or path-integrated atmospheric concentrations by receiving and analyzing spectral signals transmitted along the atmospheric path. Commonly used techniques include Fourier Transform Infrared Spectroscopy (FTIR) [45], Differential Absorption Lidar (DIAL) [46], and Differential Optical Absorption Spectroscopy (DOAS) [47]. Currently, the largest global atmospheric CH₄ column observation network is the Total Carbon Column Observing Network (TCCON) [48]. The TCCON uses FTIR to measure total column concentrations of greenhouse gases, including CH₄. Its observational data have been used for satellite data validation and for large-scale CH₄ flux inversion studies [49]. However, the TCCON’s limited spatial coverage is a drawback. As of now, the TCCON includes about 30 observation sites, with a poor coverage of desert regions and lack of stations in the Pacific and Central Asia. Two stations are located in China: Xianghe and Hefei. The Network for the Detection of Atmospheric Composition Change (NDACC) provides observations using solar FTIR measurements since approximately 30 years [50]. After five years of planning, it officially began operations in 1991 to perform high-quality measurements of atmospheric composition. There are now 118 stations, 30 of which can observe CH₄. These observational networks play a critical role in large-scale CH₄ flux inversions.

2.2.2. Satellite Observations

The wide spatial coverage of satellites offer the necessary data with spatially dense and temporally continuous observations for CH₄ flux inversion. CH₄ concentration retrieval in satellite remote sensing typically relies on the absorption characteristics of the atmosphere at specific wavelengths, primarily utilizing the shortwave infrared (SWIR) bands at 1.65 µm and 2.3 µm, as well as the thermal infrared (TIR) region near 8 µm. CH₄ retrieval algorithms mainly include empirical algorithms, physical algorithms, and neural network approaches. Among these, physical algorithms are currently the most widely used, including the Differential Optical Absorption Spectroscopy (DOAS) method [51,52], the proxy retrieval method [53], the Photon Path Length Probability Density Function (PPDF) method [54], and the Full Physics (FP) algorithm [55]. These retrieval approaches have been comprehensively reviewed by Jiang et al. [56].

Table S1 CH₄ monitoring satellite/sensors information in the Supplementary provides a detailed overview of the major CH₄ observation satellites and sensor performance [57,58,59,60,61,62,63,64]. Following the classification proposed by Jacob et al. [65], we categorize CH₄-observing satellites into area flux mappers and point source imagers. The key distinction between the two lies in their spatial resolution and the scale of CH₄ emissions they target. Area flux mappers, such as TROPOMI and GOSAT, provide a broad view of CH₄ emissions over regional to global scales, with a spatial resolution ranging from 0.1 to 10 km. These instruments are designed to quantify total emissions across large areas, making them ideal for global monitoring, emission trend analysis, and validating large-scale emission inventories. In contrast, point source imagers, including instruments like GHGSat, are specialized in detecting emissions from specific, localized point sources, such as gas wells or industrial facilities. These sensors have much finer spatial resolution, typically less than 60 m, allowing them to precisely track individual CH₄ plumes and provide detailed insights into specific emission events.

Area flux mappers include SCIAMACHY/ENVISAT, AQUA, SCISAT-1, TANSO/GOSAT, and TROPOMI/Sentinel-5P. The SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), launched by the European Space Agency (ESA) in March 2002 aboard the ENVISAT [66], was the first instrument providing CH₄ and CO₂ concentrations from space. Frankenberg et al. [58] applied a DOAS-based algorithm to retrieve CH₄ with 1.5% uncertainty.

GOSAT is part of a Japanese series of Earth observation satellites specifically designed for monitoring greenhouse gases. GOSAT was launched in 2009, GOSAT-2 in 2018 and GOSAT_GW (Global Observing SATellite for Greenhouse gases and Water cycle) was launched on 29 June 2025. GOSAT is equipped with the Thermal and Near-Infrared Sensor for Carbon Observation (TANSO), which consists of a Fourier Transform Spectrometer (FTS) and a Cloud and Aerosol Imager (CAI). The FTS is used for the detection of greenhouse gases, while the CAI collects cloud and aerosol information simultaneously to support synergistic retrieval. GOSAT provides long-term observations of XCH₄ (column-averaged dry-air mole fraction of CH₄), with an accuracy of 0.7% [60]. Wang et al. [31] used GOSAT data to invert CH₄ emissions in the Middle East from 2010 to 2017 and Parker et al. [67] published global XCH₄ maps from 2009 to 2020. However, due to the relatively small instantaneous field of view (approximately 10.5 km × 10.5 km) of TANSO, its spatial coverage is relatively sparse. This limitation constrains GOSAT’s ability to perform inversion operations at finer spatial scales.

TROPOMI (Tropospheric Monitoring Instrument) is a high-precision atmospheric monitoring instrument mounted on the Sentinel-5 Precursor satellite, which was jointly developed by ESA and the Netherlands Space Office. The satellite was launched on 13 October 2017. The primary mission of TROPOMI is to perform daily global monitoring of atmospheric constituents such as NO₂, CH₄, and O₃. The retrieval success rate averages only 3% because of clouds and dark and heterogeneous surfaces [68], but the data density is still at least 2 orders of magnitude higher than for GOSAT [17]. Offering daily global monitoring, TROPOMI achieves a fine spatial resolution of approximately 3.5–7 × 5.5 km² in the SWIR. TROPOMI utilizes spectral information near 2.3 μm for CH₄ retrieval, with a spectral resolution of 0.25 nm and an inversion accuracy of up to 0.8% [62].

MethaneSAT is a CH₄ monitoring satellite launched in March, 2024, (https://www.eoportal.org/satellite-missions/methane-sat#background, last visit 1 August 2025) but contact with the MethaneSAT mission operations was lost on 20 June 2025 (https://www.methanesat.org/project-updates/methanesat-loses-contact-satellite, last visit 3 August 2025). MethaneSAT carried a high-performance spectrometer methane sensing system that could quantify total emissions by monitoring concentrated point sources and dispersed regional sources. MethaneSAT was planned to conduct regular monitoring of most oil and gas production areas, with a detection threshold for CH₄ concentration of 3 ppb, making it the most accurate among current satellites.

Point source imagers include GHGSat, AHSI/GF-5, and VSWIR Imager/EMIT. GHGSat is a global leader in high-resolution greenhouse gas emission monitoring. Currently, there are 12 commercial satellites in orbit, each equipped with a Wide Angle Fabry-Pérot imaging spectrometer, capable of covering the shortwave infrared band from 1.63 to 1.67 μm. This satellite constellation can provide high-resolution data with a spatial resolution of 25 m, capable of identifying point sources.

GF-5 is equipped with an Airborne Hyperspectral Imaging Camera (AHSI), which effectively detects CH₄ point source emissions [69]. Equipped with a convex grating spectrometer and an advanced Offner configuration, AHSI features 330 bands, covering the 0.4–2.5 μm wavelength range. The AHSI has a spatial resolution of 30 m × 30 m.

EMIT was not initially designed for CH₄ monitoring, but has demonstrated significant capability in identifying point-source CH₄ emissions, thanks to its hyperspectral imaging technology. The instrument measures reflected sunlight across over 285 spectral bands, ranging from the visible to shortwave infrared, with a spatial resolution of approximately 60 m. In ideal conditions, EMIT has identified plumes with rates as low as 100–150 kg/h.

Tanager-1 is the first satellite of the Carbon Mapper Coalition and was launched in August 2024. This satellite was primarily designed to detect CH₄ plumes emitted from facilities or equipment, with a predicted 90% detection limit of approximately 100 kg/hr. The satellite’s imaging spectrometer (Carbon Mapper) covers over 420 bands, achieving a spatial resolution of 30 m, enabling precise location and quantification of super emitters of CH₄.

XIGUANG-004 is China’s first CH₄ monitoring satellite, launched in 2024. It is equipped with a CH₄ concentration sensor with a spatial resolution of 25 m, capable of monitoring and tracking point source CH₄ emissions.

In addition, several area flux mappers and point source imagers are planned. CO2M (Copernicus Anthropogenic Carbon Dioxide Monitoring) is an Earth observation mission initiated by the ESA under the Copernicus program. Its objective is to monitor emissions of CO₂, CH₄, and NO₂ resulting from human activities. The mission will deploy a satellite constellation consisting of three spacecraft—CO2M-A, CO2M-B, and CO2M-C—scheduled for sequential launches between 2026 and 2029, aiming to achieve global coverage capability. The three satellites will be equipped with the Combined Carbon Dioxide and Nitrogen Dioxide Imager (CO2I), capable of providing observations of CO₂, CH₄, and NO₂ at a spatial resolution of 4 km. The CO2I is a push-broom nadir scanning spectrometer capable of measuring CO₂ with an accuracy of 0.7 ppm and CH₄ with an accuracy of 10 ppb. China plans to launch several carbon monitoring satellites in the near future.

The second-generation carbon satellite, TanSAT-2, is expected to be launched in 2026. TanSat-2 is expected to incorporate a SWIR channel ranging from 2.305 to 2.385 μm, building upon the capabilities of TanSat, to enhance CH₄ detection. Additionally, the swath width is anticipated to increase from 20 km to over 100 km. Moreover, the hyperspectral satellites CHIME and SBG are scheduled for launch in 2029, each offering a spatial resolution of 30 m. The CHIME (Copernicus Hyperspectral Imaging Mission for the Environment) is a hyperspectral Earth observation mission initiated by the ESA under the Copernicus program. It will consist of two satellites, CHIME-A and CHIME-B. Each satellite will be equipped with Hyperspectral Imagers (HSI) capable of capturing data across more than 200 spectral bands, covering wavelengths from 400 nm to 2500 nm, with a spectral resolution of less than 10 nanometers. The next generation of high spatial resolution satellites is expected to play a critical role in future CH₄ flux inversions at the city scale.

2.3. Atmospheric Transport Models

The atmospheric transport model (ATM) is a mathematical framework used to simulate and predict the transport, dispersion, deposition, and chemical transformation of gases, aerosols, or pollutants in the atmosphere [70]. To estimate CH₄ emissions based on atmospheric data, the common approach is to apply three-dimensional atmospheric transport models to analyze the sensitivity of concentrations to source strengths [17]. The ATM simulates atmospheric transport on the basis of assimilated meteorological data for the observation period and a 2-D field of gridded emissions. By solving the mass continuity equation, the concentration as a function of emissions is derived, taking into account the influence of emissions, wind, turbulence, and chemical losses on the three-dimensional concentration field [71]. Eulerian models and Lagrangian particle dispersion models (LPDMs) are the two main transport models. For Eulerian models, particle concentration distributions in the atmosphere are described in a fixed spatial reference framework, while for LPDMs, the spatial coordinates track individual particles, not the global spatial grid [72].

Table 1. The main atmospheric transport model.

Coordinate System	Representative Model	Reference
Eulerian Models	GEOS-Chem	Bey et al. [73]
	TM5	Krol et al. [74]
	WRF-Chem	Grell et al. [75]
	EURAD-IM	Hass et al. [76]
Lagrangian Particle Dispersion Models	FLEXPART	Stohl et al. [77]
	HYSPLIT	Stein et al. [70]
	STILIT	Lin et al. [78]
	LES-Driven LPDM	Weil et al. [79]

lists the major atmospheric transport models.

A key strength of an Eulerian model is that it provides a complete, continuous, and mass-conserving atmosphere [71]. In terms of setting the initial and boundary conditions, the Eulerian model simplifies complex processes through grid points, making model configuration more intuitive and straightforward. An Eulerian model can obtain source–receptor relationships by using model adjoints [80]. The adjoint matrix computes the partial derivative of flux variations within a specific grid cell in response to changes in the mixing ratio at a particular time, which helps determine the optimal flux [81]. This technique provides the benefit of solving fluxes at the same resolution as the original transmission model. However, adjoint models are not available for all transport models, and their implementation is challenging.

Unlike Eulerian models, LPDMs do not compute concentration evolution on a fixed grid. Instead, they simulate the trajectories of air parcels or particles as they move through wind fields and turbulence. This allows for direct backward integration in time, enabling efficient identification of source regions that influence the concentration at a specific receptor location [71]. LPDMs have been widely applied in CH₄ inversions based on ground and aircraft data, with the restricted number of receptor sites making these models particularly efficient [82]. Given their strong handling of turbulence within the boundary layer, Lagrangian dispersion models are suitable for use at scales down to several hundreds of meters [83]. However, there are limitations to the use of LPDMs for solving inversion problems. LPDMs generally track virtual particles backward in time over periods ranging from days to several weeks, requiring separate consideration of the effects of atmospheric chemistry, transport, and surface fluxes at earlier times. Although it is possible to perform forward 3D simulations in these models, reproducing background signals such as seasonal variations, would require simulations spanning months or even years, making the computational cost prohibitively high [84].

2.4. Inversion Methods

Data assimilation is a statistical framework that integrates observational data with model simulations to optimally estimate the state of a physical system. In top-down CH₄ inversion, data assimilation plays a central role by combining atmospheric concentration measurements with atmospheric transport models, allowing for the estimation of surface fluxes that are consistent with both the observed concentrations and the governing atmospheric dynamics. The main methods for data assimilation include Bayesian optimization, Kalman Filtering(KF), and four-dimensional variational (4D-Var) methods [85,86].

2.4.1. Kalman Filter

The Kalman filter (KF) method is a recursive process based on state-space representation, which adopts a dynamic approach to update state estimates. During each time step, the next state is predicted from the system model and then refined by incorporating the latest observational data. The Kalman filter relies on the assumption of linear system dynamics and Gaussian errors. However, when dealing with nonlinear problems, variants such as the Ensemble Transform Filter (ETKF) can be used. The core formula of these methods can be written as:

$$x_i^a=x_i^f+K\left(y-H{x}_i^f\right)$$

(1)

where $x_i^a$ represents the posterior state vector, $x_i^f$ is the prior state vector, $y$ is the observational data, $K$ is the Kalman gain matrix, and $H$ is the observation operator that links surface fluxes to observational data.

In the inversion of CH₄ emissions, the EnKF generates an ensemble of state vectors by introducing random perturbations from a given initial state distribution. Subsequently, the predicted states of the ensemble members are compared to the observed data, with each member being corrected using the Kalman gain matrix for improved consistency with the observations. Chen and Prinn [87] applied a KF method to estimate CH₄ emissions from various regions. Using the Ensemble Transform Kalman Filter (ETKF) approach, Feng et al. [88] created an ensemble data assimilation system and used this system to estimate regional CO₂ fluxes over an 8-day period. ETKF differs from other ensemble Kalman filters by applying ensemble transformation and normalization, which enables the swift acquisition of the forecast error covariance matrix for specific observational data [89]. Building on previous research, Feng et al. [90] used ETKF to estimate global CH₄ emissions from 2010 to 2014. They divided the world into 44 land regions and 11 ocean regions, defining the pulse basis functions as monthly CH₄ fluxes from different emission sources within predefined geographical areas. Voshtani et al. [91] developed a parameterized Kalman filter system (PvKF), which further reduced computational costs. In this system, the error covariance prediction step deviates from the standard Kalman filter equations, utilizing a continuous formula to propagate the error covariance, which prevents the loss of error variance typically observed in the standard Kalman filter approach. Compared with the 4D-Var method, the EnKF system provides a background error covariance matrix associated with fluxes through ensemble modeling, without the need for adjoint models, making it a simple yet effective assimilation approach [92]. One limitation of EnKF is that the state vector’s resolution is directly influenced by the ensemble size, which limits its applicability in city-scale inversion studies.

2.4.2. 4D-Var Method

4D-Var is an optimization technique that operates over a time series, aiming to minimize the difference between observations and model forecasts. 4D-Var not only allows for a precise consideration of the observation times but also effectively propagates the initial background error covariance throughout the assimilation window [93]. 4D-Var minimizes the discrepancy between simulated and measured CH₄ concentrations by optimizing an objective function, which can be defined as:

$$J\left(x\right)={\left(x-x_b\right)}^T{B}^{-1}\left(x-x_b\right)+{\left(y-Hx\right)}^T{R}^{-1}\left(y-Hx\right)$$

(2)

where $x$ represents the state variables (including emissions), $R$ is the observation error covariance matrix, $x_b$ is the prior state estimate, $B$ is the prior error covariance matrix, $y$ is the observation vector, $H$ is the observation operator mapping the state space to observation space.

Methods such as gradient descent or quasi-Newton numerical optimization algorithms are commonly used to identify the model state that minimizes this discrepancy [94]. These methods reduce computational demands compared to other inversion methods and are more suitable for use in operational carbon assimilation systems. Meirink et al. [95] proposed a 4D-Var-based inversion method to optimize CH₄ emissions over the South American continent [96]. Bergamaschi et al. [85] applied three top-down inversion approaches to estimate European CH₄ emissions for 2018: the newly developed high-resolution FLEXVAR system (4D-Var, 7 km × 7 km), the sequential assimilation FLExKF system (Extended Kalman Filter, 7 km × 7 km), and the coarser-resolution TM5-4DVAR system (1° × 1°). FLEXVAR achieved the best agreement with atmospheric CH₄ observations (mean correlation r = 0.86, RMSD = 28.21 ppb), followed by FLExKF (r = 0.84, RMSD = 30.53 ppb), with TM5-4DVAR performing less well (r = 0.81, RMSD = 31.82 ppb). The FLEXVAR system is more accurately reproduced regional-scale emission patterns than TM5-4DVAR.

2.4.3. Bayesian Optimization

The Bayesian inversion method relies on Bayesian statistical principles, calculating the posterior probability distribution by combining prior knowledge with observational data [97]. First, the prior probability distribution of the emission sources is derived from information from previous studies, emission inventories, or other related data. Next, a likelihood function is constructed based on an atmospheric transport model. The likelihood function describes the probability of observing the current dataset given a set of emission parameters. Then, Bayes’ theorem is applied to convert the prior probability and likelihood function into a posterior probability distribution. Mathematically, this is expressed as:

$$p\left(\theta |X\right)={\displaystyle \frac{p\left(X|\theta \right)p\left(\theta \right)}{p\left(X\right)}}$$

(3)

where $p\left(X|\theta \right)$ is the likelihood function, $p\left(\theta |X\right)$ is the posterior probability distribution, $p\left(\theta \right)$ is the prior probability distribution, and $p\left(X\right)$ is the marginal probability of the observational data.

Many studies have applied Bayesian optimization to invert regional CH₄ emissions. Cui et al. [98] used a Bayesian least squares approach, assuming normal distributions for both observations and prior emissions, to invert CH₄ emissions in the Air Basin of California by minimizing a logarithmic cost function. Thompson and Stohl [86] developed FLEXINVERT based on Bayesian theory to estimate CH₄ fluxes in Europe for the year 2011. FLEXINVERT is capable of assessing the spatio-temporal flux distribution of any species, given that its atmospheric loss can be described using a linear process [86]. This model is versatile, applicable at continental, regional, and local scales. Thompson et al. [16] conducted their research on a larger regional scale, constructing a cost function based on Bayesian theory and assuming Gaussian-distributed uncertainties in prior emissions to invert CH₄ emissions over East Asia for multiple years. A key advantage of the Bayesian method lies in its capability to handle uncertainties and provide probabilistic interpretations of parameter estimates. The posterior probability distribution allows for direct assessment of parameter uncertainty and correlations between parameters, which not only provides the most probable estimate of CH₄ emissions, considering the new observational data, but also quantifies the uncertainties in the estimated emissions.

2.5. Applications to City Scale Inversions

2.5.1. Current Status of City-Scale Inventories

Top-down CH₄ flux estimation methods have proven effective at global and regional scales [4]. However, city-scale CH₄ flux inversion studies typically require gridded emission inventories with a spatial resolution of 5–10 km [99], which poses new challenges for the spatial distribution of the inventories. Currently, city-scale inversion studies typically downscale the EDGAR or, for the U.S., the Gridded Methane GHGI to an appropriate spatial resolution and use it as the prior emission inventory [19,20]. Although such approaches can yield high-resolution emission inventories at the city scale, the high spatial heterogeneity of urban emission sources poses a significant challenge. Global inventories like EDGAR typically have an original resolution of 0.1°. While this resolution is relatively fine for global-scale analyses, it remains insufficient to accurately represent small-scale emission hotspots within urban areas or from individual facilities, many of which have spatial extents of only a few hundred meters to a few kilometers. As a result, emissions from point or line sources (e.g., landfills, wastewater treatment plants, gas distribution leaks) are spatially diluted over large grid cells, and their exact locations may be misrepresented due to aggregation and proxy-based allocation methods used in inventory construction. Downscaling to higher resolutions can improve spatial detail, but it cannot fully correct for the original spatial misallocation or omission of sub-grid-scale sources inherent in the coarse input data. Studies using EDGAR or the Gridded Methane GHGI for city-scale inversions consistently show substantial discrepancies between inversion results and prior inventories [19,100]. These differences are discussed in detail in Section 3.1. For the vast majority of cities, high-resolution local emission inventories are lacking. In China, while all provinces report aggregated CH₄ emissions, gridded emission maps are not provided. There is an urgent need to develop localized city-scale gridded emission inventories.

When the inversion domain is defined by administrative city boundaries, natural sources must also be included in the prior emission inventory. Suburban areas of some cities contain natural wetlands or extensive forested regions, and natural sources such as termites and biomass burning should be taken into account. However, existing inventories of these natural sources typically have much coarser spatial resolution, as discussed in Section 2.1. Therefore, improving the spatial resolution of the CH₄ natural source gridded inventory is also an urgent problem to be solved.

2.5.2. Application of Urban Observation Networks and Satellites in City Scale Inversion

Global ground-based observation networks, such as the NOAA/GML, TCCON, and AGAGE, play a vital role in assessing the global carbon budget and monitoring long-term climate change. However, they are not designed for monitoring CH₄ emissions at the city scale. Observation stations in these networks are typically located in remote areas with minimal interference from local sources—such as mountaintops, coastlines, or plateaus—with the aim of capturing regional or even global average concentration levels. The distances between these stations can span several hundreds to over a thousand kilometers, making them unable to capture concentration gradients within and around city areas. This sparse spatial distribution significantly limits their ability to constrain CH₄ emissions at the city scale.

Hence, for the application in city-scale CH₄ inversion studies, local ground-based observations are needed which are capable to capture contributions from typical sources in that city. To achieve this, intra-city observation networks are established [101] and sampling strategies are developed for mobile measurements across a city using vehicle-mounted sensors [102,103,104,105] or aircraft measurement campaigns [106,107]. For example, the INFLUX project established a dense tower-based observation network in Indianapolis, using Picarro instruments to measure CH₄ concentrations at various locations across the city [108]. Picarro analyzers (based on CRDS technology) are widely used in city-scale CH₄ observations due to their high sensitivity at the ppb level and temporal resolution on the order of seconds [107]. Lopez-Coto et al. [106] conducted regional-scale CH₄ emission estimates over the Washington–Baltimore area using aircraft-mounted CRDS instruments. The study illustrates the strength of airborne in situ observations for rapidly covering large urban areas from five flights over a two-week winter campaign, each spanning the full planetary boundary layer (PBL) and traversing both Washington, DC, and Baltimore along multiple horizontal transects. Leifer et al. [105] combined airborne remote sensing data, acquired by an airborne thermal infrared Mako imaging spectrometer, with contemporaneous meteorological and CH₄ concentration data from a ground based mobile system, SISTER™ (Standard Instrumentation Suite: Truck Enabled for Response) collected in the Los Angeles Port area. CH₄ emissions derived from the ground-based in situ data and from the Mako remote sensing data were in good agreement. Kohler et al. [104] conducted mobile measurements of CH₄ mixing ratios in Münster, Germany, using a modified cargo bicycle equipped with an LI-7700 open-path CH₄ gas analyzer, and quantitatively assessed urban CH₄ emissions. Umezawa et al. [109] conducted a three-week mobile survey in the Tokyo metropolitan area, using a mid-infrared spectrometer (MIRA ULTRA) for high-precision, real-time monitoring of CH₄ and ethane (C₂H₆) concentrations in the atmosphere. The study established empirical equations based on controlled release experiments, converting measured CH₄ excess concentrations into leakage point emission rates. These rates were then used, along with Leak Point Density and the observational coverage area, to estimate the regional average flux and total annual emissions. Ground-based remote sensing techniques such as FTIR measurements are used in a network in Indianapolis to effectively estimate CH₄ emissions from that city [100].

Owing to their broad spatial coverage, satellite observations hold significant potential for methane flux inversion at the city scale. Notably, the TROPOMI satellite has been successfully applied to CH₄ emission inversions in multiple cities [20,21,26,110]. In city scale CH₄ flux inversion, TROPOMI provides a large volume of observational data. For example, the study by Nesser et al. [111] utilized a total of 2,919,358 observations across North America in 2019. de Foy et al. [21] processed TROPOMI-derived XCH₄ data that were specifically oversampled to 1 km grids to estimate CH₄ emissions from 61 urban regions worldwide. This oversampling approach enhances spatial resolution, improves source attribution, and better aligns with high-resolution inversion frameworks. Hemati et al. [20] employed TROPOMI XCH₄ data in combination with the Integrated Methane Inversion (IMI) cloud platform to estimate 2021 CH₄ emissions from major North American cities such as Toronto, Montreal, and Los Angeles, with the number of valid observations per city ranging from 872 to 10,648.

2.5.3. Challenges of Atmospheric Transport Models at the City Scale

At the city scale, due to the complex effects of buildings, roads, and other urban infrastructure on air flow, the accuracy of atmospheric transport models is often limited. Small-scale transport errors can lead to substantial variations in CH₄ emission inversion results. One approach to addressing this issue is the use of higher-resolution wind field data to drive atmospheric transport models. For example, Cui et al. [98] used high-resolution meteorological fields simulated by the Weather Research and Forecasting (WRF) model to drive a Lagrangian particle dispersion model for the inversion of CH₄ emissions in California. Time-averaged winds generated by the WRF model are used instead of instantaneous wind to reduce uncertainties in the Lagrangian trajectories in complex terrain [112]. Yadav et al. [113] generated high-fidelity meteorological fields for the South Coast Air Basin using a high-resolution, triple-nested configuration of the WRF model, with horizontal resolutions of 12 km, 4 km, and 1.33 km, and 51 vertical levels. These meteorological fields were coupled with the STILT model to enhance the representation of local wind fields and concentration gradients. The simulated wind speeds were consistent with Aircraft Communications, Addressing, and Reporting System (ACARS) observations, with a mean bias of less than 0.5 m/s and a mean potential temperature error of less than 0.5 K.

Another approach is the enhancement of the model’s ability to simulate small-scale processes. Bréon et al. [114] developed a transport model with a resolution of 2 km, which revealed the complex boundary layer structures in urban core areas and addressed the challenge of accurately simulating concentration variability caused by local wind fields. Lauvaux et al. [115] used the mesoscale meteorological model WRF-Chem with three nested grids of varying resolutions, which resulted in the enhancement of the simulation accuracy within the inversion domain.

2.5.4. Applicability of Data Assimilation Methods at the City Scale

The applicability of different data assimilation methods at the city scale must take into account both computational efficiency and the treatment of uncertainty.

The 4D-Var method formulates the inversion problem as a cost function minimization, offering high computational efficiency. For instance, Pandey et al. [116] reduced the computation time by an order of magnitude by applying physical parallelization techniques within the TM5-4DVAR framework. However, this approach typically yields only the optimal flux estimate without directly providing posterior uncertainty. Estimating uncertainty requires additional procedures, such as constructing and iteratively solving an adjoint model, which can be computationally expensive—particularly when dealing with complex nonlinear models [96].

Unlike the 4D-Var, the Kalman filter (KF) does not directly construct a cost function to optimize model parameters [117]. In the Ensemble Kalman Filter (EnKF) method, posterior uncertainty in the system state is not obtained analytically but is instead approximated using the statistical properties of an ensemble of samples. Specifically, the ensemble mean represents the optimal state estimate, while the sample covariance matrix serves as an approximation of the posterior covariance. This method theoretically embodies the principles of Bayesian inference. However, in practice, it faces a critical challenge: when the ensemble size is limited, spurious correlations and underestimation of covariance may arise, significantly undermining the reliability of posterior uncertainty estimates. Conversely, increasing the ensemble size can substantially increase computational costs.

Recently, a hybrid assimilation approach that integrates the ensemble and variational methods has been steadily advancing. The En4DVAR technique was developed by Liu et al. [118], integrating an ensemble-based approach with a flow-dependent background error covariance matrix derived from ensemble forecasts. The algorithm uses 4D-VAR optimization to yield a balanced analysis. Zhao et al. [119] developed GONGGA-CH₄ based on hybrid assimilation techniques and applied it to CH₄ emission inversion at the national scale. To solve the nonlinear inverse problem with high precision, the GONGGA-CH4 system utilizes the NLS-4DVar algorithm [120]. A major benefit of the En4DVAR method over conventional 4DVAR techniques is its ability to bypass the requirement for tangent linear and adjoint models in its development and application. This feature makes it promising for future application in city-scale inversion studies.

Compared to 4D-Var and Kalman filtering methods, Bayesian methods are more suitable for city-scale inversions. The Bayesian approach explicitly constructs prior and observational error covariance matrices to produce a full posterior probability distribution, allowing direct estimation of the mean and covariance of emission fluxes. This makes it well-suited for quantifying uncertainty in urban environments where observations are sparse and emission sources are complex. Thompson et al. [121] used four models to invert CH₄ emissions across Europe. Their results showed that, compared to TM5-4DVAR and CTE, which is developed based on the EnKF method, the Bayesian-based FLEXINVERT model has greater effective degrees of freedom, providing more flexibility in flux optimization and reducing the uncertainty of the results. Brunner et al. [122] compared four independent inversion model systems (EMPA, EMPA2, NILU, and UKMO) to estimate emissions of hydrofluorocarbons (HFC-125 and HFC-134a) and sulfur hexafluoride (SF6) in Europe. The results showed that the NILU system, which combines an LPDM with a Bayesian inversion framework, achieved the greatest and spatially most consistent reduction in uncertainty. Due to its advantages in handling uncertainties, the Bayesian approach has been adopted in nearly all city-scale CH₄ inversion studies. Jones et al. [100] used a Bayesian inversion framework to simultaneously estimate city emissions and background gas concentrations, effectively addressing the impact of background uncertainty on inversion results. Lopez-Coto et al. [106] applied a Bayesian approach using ensemble inversion techniques to quantify sampling bias and uncertainty, thereby enhancing the robustness of the inversion results.

3. Top-Down Inversion of CH₄ Flux at City Scales

Figure 3 presents the cumulative number of publications on top-down CH₄ flux inversion studies at different spatial scales from 2012 to June 2025. The data were retrieved from the Web of Science Core Collection using the SCI-EXPANDED and SSCI indexes. Figure 3 shows that the global scale dominates the research landscape, followed by the regional scale, both showing a steady increase in publication volume. In contrast, studies focused on the city scale remain scarce throughout the observed period, highlighting a significant research gap in fine-scale CH₄ flux quantification. This section focuses on the differences between top-down inversion results and bottom-up inventory approaches at the city scale, and analyzes the uncertainties associated with the inversion outcomes.

3.1. CH₄ Flux Inversion Results at the City Scale

Studies of top-down inversion of CH₄ emission at the city scale are relatively scarce, as compared with those at global and regional scales. Multiple studies for the same city are rare, inhibiting comparison between different results. Therefore, we compared top-down inversion results with bottom-up emission inventories.

Top-down inversion studies at the city scale consistently reveal that traditional bottom-up inventories systematically underestimate CH₄ emissions. For example, a study using annual emission data for 12 major cities in the U.S. in 2022, shows that emissions estimated using top-down inversion based on TROPOMI observations were on average approximately 80% higher than those reported in the EPA’s Greenhouse Gas Inventory (GHGI), with discrepancies ranging from 22% to as high as 290% [123]. Only Los Angeles and Cincinnati showed higher prior inventory estimates, with positive biases ranging from 32% to 37% [123]. The study performed sectoral attribution of the inversion results based on the contribution ratios of prior emission sources. The findings indicated that landfills are the primary reason for the underestimation of urban CH₄ emissions. In inventories, reported landfill CH₄ emissions depend strongly on the assumed landfill gas recovery efficiency. This parameter refers to the fraction of total generated CH₄ that is captured for flaring or energy use rather than released to the atmosphere. Except for Los Angeles, the average recovery efficiency assumed in our analysis was 38%, substantially lower than the 70% reported in the U.S. GHG. This lower recovery efficiency implies greater fugitive emissions from landfills.

The inversion results reported by Hemati et al. [20] showed even greater discrepancies. Their TROPOMI-based inversion of CH₄ emissions across six major North American cities showed that prior inventories substantially underestimated emissions in Toronto, Montreal, Los Angeles, and especially Houston, where the correction factor reached as high as 6.2. In contrast, New York showed only a slight underestimation, while Mexico City was the only case where prior emissions were overestimated. Overall, the inversion-derived correction factors ranged from 0.22 to 6.2, reflecting large spatial variability in the accuracy of prior estimates. The trends reported by Hemati et al. [20] for New York and Houston are consistent with those of Wang et al. [123], whereas the results for Los Angeles differ in sign. However, because Hemati et al. did not perform a sectoral attribution of CH₄ emissions, the underlying reasons for this discrepancy cannot be readily determined.

de Foy et al. [21] used TROPOMI data from 61 cities worldwide and applied a two-dimensional Gaussian model to estimate urban CH₄ emission intensities, finding values 3 to 4 times higher than those reported in the EDGAR v6 inventory. The study further revealed that CH₄ emissions were positively correlated with untreated domestic wastewater, but showed no significant correlation with sectoral emissions reported in the inventory, highlighting a substantial underestimation of diffuse sources such as wastewater systems in EDGAR. Hu et al. [19] established the first tower-based CH₄ observation network at the city scale in Hangzhou, China, consisting of three sites. Their results showed that the bottom-up inventory overestimated total citywide emissions by 36%, including a 47.1% overestimation of CH₄ from waste treatment. However, the inventory significantly underestimated certain monthly emission peaks, particularly those from waste sources, which exhibited strong temperature sensitivity. In contrast, EDGAR does not account for the feedback mechanism of temperature-driven seasonal variation in emission factors, leading to structural bias.

Overall, the discrepancy between top-down inversion results and bottom-up inventories at the city scale is substantial, often exceeding prior estimates by a large factor. While global and national inventories may provide reasonable estimates when aggregated over large regions, as they are derived from extensive pools of integrated CH₄ concentration data, they are less effective for guiding mitigation at finer spatial scales. Effective emission reduction requires the identification of large emitters, including not only concentrated sources such as production sites and coal mines, but also distributed urban sources such as landfills and natural gas distribution systems. For policy and mitigation planning, improving the accuracy of city-scale emission estimates is therefore critical to enable targeted actions that can achieve meaningful reductions in atmospheric CH₄ concentrations.

3.2. Uncertainty Analysis of CH₄ Flux at the City Scale

Uncertainty analysis is central to understanding the credibility of top-down inversion results at the city scale. It not only affects the scientific robustness of research findings but also directly influences the utility of emission monitoring in supporting policymaking and evaluating mitigation efforts. The U.S. National Academies identified the lack of sufficient quantification of uncertainties as one of the major barriers in current urban greenhouse gas inversion studies, leading to a “credibility gap” in their policy relevance [124]. The significant discrepancies between top-down and bottom-up approaches further underscore the substantial uncertainty in estimating CH₄ emissions at the city scale.

Currently, there are two primary approaches for quantifying the uncertainty of inversion results. For Bayesian-based methods, the uncertainty can be directly derived from the posterior error covariance matrix [125]. The Bayesian posterior uncertainty quantifies how the observation and prior errors impact the posterior flux estimates. Another approach involves performing ensemble inversions using different observational datasets, prior emission inventories, atmospheric transport models, or other inversion-related parameter configurations. The spread of the ensemble is then used to represent the uncertainty of the inversion results. In recent years, numerous studies have conducted quantitative analyses of inversion uncertainties at the city scale. Nesser et al. [111] conducted a Bayesian inversion using TROPOMI satellite data for 95 U.S. cities and reported an uncertainty of 11% in the total emission estimates. To assess the impact of prior flux spatial distributions on inversion results, Jones et al. [100] conducted a sensitivity analysis using three different emission patterns: the default HESTIA (High-Resolution Fossil Fuel CO₂ Emissions Estimation System) distribution, a population density-weighted distribution, and a road density-weighted distribution. While keeping the total emissions constant, the inversion results showed significant variation: diffuse emissions were estimated at 73.3 ± 22 mol s⁻¹ under the HESTIA distribution, increased to 117.9 ± 28 mol s⁻¹ under the population-weighted distribution, and rose to 301.4 ± 70 mol s⁻¹ under the road-weighted distribution—equivalent to 1.7, 2.7, and nearly 7 times the prior estimate, respectively. These findings demonstrate the high sensitivity of inversion outcomes to prior spatial distributions and underscore the importance of constructing and testing multiple prior configurations to ensure robustness, particularly when observational data are limited.

The study by Huang et al. [126] also demonstrated that prior emission inventories are a major source of uncertainty in inversion results. Using a geostatistical inversion framework, they integrated CH₄ measurements from four tall towers with outputs from the STILT Lagrangian particle dispersion model. They designed an 18-member simulation ensemble that combined three prior emission inventories (EPA, EDGARv42, EDGARv432), three meteorological drivers (the High-Resolution Rapid Refresh, the Noth America Regional Reanalysis, the Global Data Assimilation System), and two background concentration schemes (trajectory-based and constant-value approaches) to systematically evaluate the impacts of transport error, background settings, and prior variability. The inversion estimated a mean monthly urban CH₄ emission of 39 ± 9 Gg/month, corresponding to an uncertainty of 23%. Prior inventories had a significant influence: the posterior emissions were 2.0 ± 0.4 times higher than the ensemble mean prior estimate (including wetland sources), and as much as 3.1 ± 0.7 times higher than the EPA inventory alone. In addition, seasonal variability was identified as a key contributor to uncertainty, with winter CH₄ emissions significantly exceeding summer levels, showing a maximum difference of 41%.

Lopez-Coto et al. [106] estimated wintertime CH₄ fluxes for the Washington, DC–Baltimore metropolitan area and found that daily variability was the dominant source of uncertainty (28%), surpassing methodological uncertainty (24%). The study emphasized that the observed day-to-day variation in emission estimates was not due to the inversion method itself but was largely driven by the aliasing effect—caused by the spatiotemporal mismatch between observations and major emission sources such as power plants and traffic. The aliasing effect refers to the misinterpretation of short-term fluctuations in source emissions as inter-day variability in total emissions, resulting from uneven temporal and spatial coverage of airborne measurements. This finding underscores that single flight campaigns often fail to capture diurnal variation, and such irregular sampling can lead to significant error propagation.

In the study by de Foy et al. [21], urban CH₄ fluxes were estimated using a two-dimensional Gaussian model, and a two-tiered sensitivity analysis was conducted to identify sources of uncertainty. In the first level, the authors tested combinations of various satellite data filtering strategies—including quality assurance (QA) flags, pixel water masking, and observation band positions—resulting in 36 simulation cases per city. The second-level analysis, based on the optimal configurations from the first tier, further explored 18 sensitivity scenarios by combining model scale parameters, the number of usable pixels, and the degree of water masking. The results indicated a median uncertainty of 15% in the second-level analysis, with an interquartile range of 10–22%. The study concluded that the dominant source of uncertainty arose from the coupled error between the Gaussian model’s scale parameter and wind speed estimation.

Overall, due to uncertainties stemming from prior inventories, transport models, observations, and other factors, the uncertainty in CH₄ emission estimates at the city scale ranges from approximately 11% to 28% [106,111]. This is significantly higher than the global inversion uncertainty, which is around 3% [4]. While this level of uncertainty may appear comparable to retrieval errors for other atmospheric quantities, city-scale applications place more stringent demands on accuracy. Detecting emission reductions of 10–20% over a few years, attributing observed changes to sources versus sinks, and verifying progress toward mitigation targets all require annual uncertainties closer to 10–15% [15,101,127]. In addition, urban environments often contain strong but localized sources such as landfills or wastewater facilities, where accurate quantification is essential to evaluate the effectiveness of mitigation measures. Therefore, reducing inversion uncertainties below current levels is critical for making CH₄ flux estimates scientifically robust and policy relevant in urban contexts.

For the uncertainty sources, atmospheric transport, prior emission, and inversion algorithms are all the sources of uncertainty for CH₄ fluxes. Beyond the major uncertainty sources, spatial resolution can amplify uncertainties at several stages, including observation footprints, atmospheric transport model grids, and prior emission grids. When observation systems use large pixels, spatial averaging substantially reduces the detectability of intra-urban emission variability. For example, the TROPOMI satellite, with a moderate resolution of 3.5–7 × 5.5 km, can reliably constrain total city-scale emissions, but at finer city scales it smooths source heterogeneity and leads to an overreliance on prior emission distributions in inversions [111]. The grid resolution of forward transport models also affects inversion outcomes. At coarse resolutions of 4–12 km, plumes in complex terrain and local circulations become overly diluted and may produce spurious leakage across grid cells. In contrast, inversion studies in California using nested WRF simulations at 1.3 km resolution better resolved emission features in the Los Angeles Basin and markedly improved the simulation of transport and boundary-layer structure [128]. Moreover, the spatial distribution and grid resolution of prior emissions are critical determinants of uncertainty. A study in Indianapolis found that when road density was used as a spatial proxy instead of the HESTIA inventory, posterior estimates of diffuse sources were amplified by several times. This aggregation error and spatial leakage effect underscored the strong influence of prior distributions on inversion results [100]. However, we still believe that the uncertainty of the wind field is the greatest source of uncertainty in the inversion of CH₄ flux.

4. Future Prospects of Coordinated Satellite–Ground City-Scale CH₄ Flux Inversions

With the growing demand for city climate governance, city-scale CH₄ flux inversion is advancing toward a new phase characterized by higher spatiotemporal resolution and improved accuracy. We propose a potential future framework for city-scale CH₄ flux inversion, which integrates city-scale emission inventories, coordinated satellite and ground-based observations, and inversion optimization techniques (see Figure 4).

Firstly, the primary sources of CH₄ should be identified based on the city’s development context, and a high-resolution local emission inventory should be established. To better represent complex city wind fields and dispersion processes, further development of multi-scale nested atmospheric transport models is needed, complemented by machine learning techniques to obtain more precise SRRs (Source–Receptor Relationships). In terms of data acquisition, more observational information should be obtained by integrating satellite remote sensing with ground-based monitoring networks. Through data assimilation systems, observational data can be used to optimize prior inventories. Additionally, isotopic techniques can be employed to trace CH₄ sources, thereby enhancing the source attribution and reliability of inversion results. Based on inversion outcomes, CH₄ emission inventories can be dynamically updated, providing assessment and decision-making support for local governments, ultimately enabling a complete loop from monitoring and assessment to policy implementation and mitigation.

4.1. Coordinated Satellite–Ground Observations

City CH₄ flux inversion relies on high-precision observations of atmospheric concentrations of CH₄ [98,107]. Commonly used methods include in situ measurements at observation stations and airborne surveys. In situ measurements and ground-based remote sensing provide long-term, high-frequency, and high-precision CH₄ observations, playing a critical role in city-scale CH₄ flux inversions [107]. However, due to the limited number of observation stations, these methods primarily capture local emission characteristics and are insufficient for representing city-wide emission patterns. Airborne measurements, by flexibly adjusting flight paths, can acquire CH₄ concentrations over specific areas and altitudes, thereby providing vertical profiles of CH₄ distribution. However, airborne observations are not suitable for continuous monitoring and are expensive, making them more appropriate as a complementary approach to ground-based measurements. The rapid advancement of satellite remote sensing, particularly with missions such as TROPOMI, has opened new opportunities for city-scale inversions [100,111]. Satellite observations offer broad spatial coverage. Instruments like TROPOMI provide near-daily global coverage and large volumes of CH₄ data, making them particularly suitable for cities in developing countries where ground-based monitoring networks are limited. However, urban CH₄ sources are highly heterogeneous, including gas leaks, wastewater treatment plants, and traffic emissions. These sources are typically confined to spatial scales of hundreds or even tens of meters—much smaller than the size of a single TROPOMI pixel. Although point-source imagers like GHGSat offer much higher spatial resolution, their limited swath width, sparse pixel count, and infrequent revisit times hinder their ability to provide continuous, city-wide monitoring.

Coordinated satellite–ground based observations may represent a promising direction for future development, as the two approaches are complementary and together can advance city-scale CH₄ flux inversion. On the one hand, combining multiple observation techniques provides a richer dataset. Lu et al. [129] found that the joint inversion of GOSAT and ground-based observation data yielded the best fit with the observation ensemble, with the addition of GOSAT data providing more than twice the independent information compared to using only ground-based data. Ground-based instruments can also conduct coincident measurements during satellite overpasses, thereby calibrating column-averaged satellite data products and reducing measurement uncertainties. Using XCH₄ observations from the TCCON sites at Hefei and Xianghe, Hong et al. [130] developed a spatiotemporal co-location and statistical validation framework to evaluate GOSAT systematic bias and random error relative to ground-based measurements, as well as their evolution across temporal and spatial scales. On the other hand, coordinated satellite–ground observations enable multi-platform validation of emission estimates, thereby improving flux-estimation accuracy and reducing systematic uncertainty. Mastrogiacomo et al. [131] employed an integrated framework combining satellite remote sensing, ground-based mobile surveys, and dispersion modeling to conduct quantitative analysis and validation of natural gas pipeline leaks in Cheltenham, United Kingdom. The study used GHGSat observations to monitor natural gas leaks and applied the Integrated Mass Enhancement (IME) algorithm to derive CH₄ emission fluxes. Subsequently, a mobile ground-based observation platform sampled CH₄ plumes along roadways, and fluxes were retrieved using a Gaussian plume model, providing an independent validation of the satellite-derived estimates. To further reduce systematic biases between observation systems, they employed the NAME model to assimilate both satellite and ground-based measurements, yielding a range of flux estimates. The results showed that although the model-derived fluxes were slightly lower than both satellite- and ground-based estimates, they consistently fell within the 1σ uncertainty range, demonstrating that multi-source observations can achieve quantitative consistency within a unified physical framework.

The advancement of coordinated observations likewise faces challenges. Building high-density ground-based observation networks in cities is costly; monitoring stations therefore need to be sited strategically. Differences in the spatiotemporal resolution of satellite and ground-based data can compromise the accuracy of inversion results; how best to co-locate and reconcile these observations remains an open question. Moreover, evaluating the influence of alternative observation-system configurations on inversion outcomes is essential. Regarding the first question, existing mesoscale weather networks (mesonets) that already provide dense meteorological observations could represent a promising backbone if equipped with calibrated CH₄ sensors, offering a cost-effective way to enhance coverage and support improved inversion performance. For the remaining issues, additional research will be required in future studies.

4.2. Application of Artificial Intelligence Technology

The introduction of artificial intelligence (AI) has brought about a turning point for computationally intensive meteorological models and assimilation inversion. AI is widely applied in atmospheric transport models, ranging from specialized small-scale models [132] to large-scale systems, such as the AIFS (Artificial Intelligence Forecasting System) and Fuxi model [133,134]. For the SRRs in the top down inversion, Fillola et al. [135] reported gradient-boosted regression trees to emulate SRRs traditionally simulated by LPDMs. This significantly reduces computational demand by eliminating the need for individual LPDM runs for each data point, thereby enabling high-resolution, satellite-driven inversions at city scale. Building on this concept, Dadheech et al. [136] developed FootNet, a deep learning–based surrogate model capable of generating kilometer-scale footprints. This model outperformed full-physics atmospheric transport models in inversion accuracy while being up to 650 times faster on equivalent hardware. This provides strong support for effectively solving the SRR calculation problem.

In the field of assimilation, the inclusion of AI has had an impact on traditional methods. These AI-driven approaches are continuously improving spatial resolution and advancing toward end-to-end forecasting frameworks [137]. By using AI methods, CH₄ emissions have been extracted directly from spectral information from some high-resolution hyperspectral satellite sensors. Vaughan et al. [138] established a scalable framework (MARS-S2L) combining machine learning (ML) models with satellite observations from Sentinel-2 and Landsat imagery, to provide near-real-time detection of large emission events at a global scale. This method has basically achieved end-to-end CH₄ emission detection, but it has so far been applied only to point source detection [138,139]. Given the advantages of strong nonlinear fitting and high-speed computing using AI, it is an expected direction to establish an efficient inversion method of emission distribution in the city from direct measurement by satellites.

4.3. Methods for Distinguishing CH₄ Sources

The core reason why top-down inversion is considered less advantageous than bottom-up methods lies in the fact that the area CH₄ land-atmosphere flux obtained by the top-down method cannot distinguish between natural and anthropogenic sources. Urban CH₄ emission sources are highly complex, necessitating the development of methods capable of effectively distinguishing and quantifying the contributions of individual sources. The main approaches currently used for source apportionment include stable isotope analysis, co-emitted tracer methods, and imaging spectroscopic remote sensing.

The stable isotope method is currently the principal approach for source apportionment. Carbon isotopes provide valuable information for improving source attribution. CH₄ generated through the thermal breakdown of organic matter during oil and gas formation typically has higher carbon isotope ratio of CH₄ ($\delta$¹³C-CH₄) and hydrogen isotope ratio ($\delta$¹³C-CH₄) values than CH₄ produced by microbial processes [140]. At large scales (regional or national), observations of CH₄ and $\delta$¹³C-CH₄ can be combined with top-down inversion models to estimate CH₄ emissions. Quay et al. [141] used the $\delta$¹³C-CH₄ and the hydrogen isotope ratio ($\delta$D-CH₄, D/H) as tracers for identifying sources and sinks. Thompson et al. [16] utilized $\delta$¹³C-CH₄ and CH₄ mole fractions to assess how different source types contribute to the overall CH₄ emissions in China, based on a Bayesian inversion approach. At urban or local scales, source-specific isotopic signatures are typically derived using linear regression extrapolation with Keeling plots or Miller–Tans plots, enabling the differentiation and quantification of distinct source categories. Zazzeri et al. [142] continuously recorded CH₄/CO₂ concentrations using a Picarro CRDS on the rooftop of King’s College London, and collected samples with an autosampler for isotopic analysis. Applying the Miller–Tans regression method, they estimated a source $\delta$¹³C-CH₄ signature of −45.7 ± 0.5‰, consistent with natural gas leakage, revealing that inventories substantially underestimated urban natural gas emissions. Defratyka et al. [143] conducted 17 mobile surveys in Paris and used isotopic analysis to distinguish CH₄ emissions from natural gas leaks, sewer pipelines, and combustion sources.

The co-emitted tracer method distinguishes emission sources based on the characteristics of gases emitted alongside methane: fossil fuel–related methane is typically accompanied by ethane (C₂H₆), propane, and other light alkanes, whereas biogenic methane contains little to none of these components. Therefore, source attribution can be achieved by examining the correlation between CH₄ and ethane (ΔC₂H₆/CH₄ slope), or between CH₄ and CO/CO₂. A key aspect of this approach is determining local end-member ratios, i.e., the characteristic values of specific indicators for each emission source. Hopkins et al. [144] conducted mobile surveys in Los Angeles and, by combining measured end-member C₂H₆/CH₄ ratios from various sources, attributed 213 urban hotspots, finding that 58–65% were associated with natural gas. Peischl et al. [145] used aircraft observations in combination with multiple light alkanes (C₂–C₅) and showed that methane emissions in Los Angeles were dominated by fossil sources, with total emissions exceeding those reported in official inventories. Plant et al. [146] conducted aircraft transect measurements across several cities in the eastern United States, using CH₄–CO/CO₂ correlations constrained by ethane slopes to show that urban methane emissions were primarily from natural gas systems. In addition, certain tracers have proven particularly effective in identifying specific sources. For example, Sulfur hexafluoride (SF₆) is often used as a tracer gas to quantify enteric CH₄ emissions from ruminants [147,148].

The imaging spectroscopic remote sensing method employs airborne or satellite spectrometers operating in the shortwave infrared to detect CH₄ plume enhancements. Source emission rates are retrieved using techniques such as integrated mass enhancement, cross-sectional flux methods, or Gaussian plume modeling, and subsequently matched with facility geoinformation to identify and quantify large point sources. Duren et al. [127] conducted systematic aerial surveys with AVIRIS-NG over 272,000 facilities in California, detecting more than 500 point sources. They found that the top 10% of emitters accounted for ~60% of total emissions, and identified landfills as the dominant sectoral source. Cusworth et al. [149] carried out repeated aerial surveys over hundreds of landfills across 18 U.S. states, confirming the persistence of strong emissions. Their findings, consistent with airborne in situ measurements, indicated that conventional inventories severely underestimate landfill emissions.

In future satellite–ground coordinated frameworks for city CH₄ flux inversions, ground-based observation networks could simultaneously collect $\delta$¹³C-CH₄ and other tracer data, enabling quantitative source apportionment of emissions from different urban sectors. This will provide a solid foundation for scientifically sound, targeted, and verifiable strategies for urban CH₄ mitigation and management. Although challenges remain in terms of analytical precision and model complexity, the prospects for this field are promising.

5. Conclusions

With increasing urbanization, the contribution of city CH₄ emissions has gained significance [19]. Due to the complexity of city CH₄ sources, bottom-up inventory approaches often fail to account for all emission sources, leading to an underestimation of total CH₄ emissions. Top-down inversion methods use atmospheric concentration measurements to constrain emissions and are capable of capturing overlooked sources. However, the limited resolution of prior emission inventories, the reliance on single-mode observation systems, and the inaccurate simulation of local wind fields pose significant challenges for city-scale CH₄ flux inversions. This paper provides an overview of CH₄ flux inversion at the city scale from several aspects: top-down atmospheric inversion methods, CH₄ emission estimation and associated uncertainties and future directions for CH₄ flux inversion at the city scale.

For prior fluxes, the EDGAR emission inventory, with its relatively high spatial resolution, is the preferred data source for estimating anthropogenic emissions at the city scale, while WetCHARTs serves as the primary inventory for natural source emissions. In terms of observational data, ground-based in situ measurements provide the highest possible precision and continuous observations with temporal resolution determined by the method, whereas satellite observations offer broader spatial coverage at the cost of accuracy and temporal resolution. For inversion methodologies, hybrid approaches show comparative advantages for city-scale CH₄ inversion, while Bayesian methods offer unique capabilities in resolving temporal backward footprints at individual observation points. Statistics from the literature show that CH₄ flux inversion studies at the city scale are scarce compared to global and regional scales. Analysis of existing city-scale inversion studies reveals a significant disparity between the CH₄ emission estimates derived from top-down inversion methods and bottom-up inventory methods, with differences reaching several times the estimates. The uncertainty in city-scale CH₄ flux inversions ranges from 11% to 28%, with sources of uncertainty including prior inventories, observational data, transport errors, and model parameters. These results suggest that improvements are necessary at the city level, and extensive further research is required. Future research should prioritize the integration of satellite and ground-based observations as key top-down inversion constraints, leveraging AI-driven algorithms to accelerate real-time processing, and enhancing source attribution through carbon isotope observations, which is crucial for CH₄ emissions accounting.