The impact of atmospheric observations on CH₄ emission estimates is quantified using a Bayesian inversion framework, in which prior information on monthly gridded surface emissions is updated by observational constraints through atmospheric transport modelling. The Kalman gain matrix (K) determines the relative influence of observations and prior information in the posterior update (Rodgers, 2000; Rayner et al., 2019): 1K=BHTHBHT+R-1 where B denotes the prior emission error covariance matrix, H is the Jacobian matrix (also known as footprint or transport sensitivity) linking surface emissions to XCH₄ observations, R is the observational error covariance matrix. The observational error covariance R is prescribed as diagonal, with a constant standard deviation of 5 parts per billion (ppb) as the default value, consistent with the expected retrieval precision of EM27/SUN spectrometers (Doc et al., 2026). Doing this, we neglect the contributions of H (i.e., the model error) and of the sub-monthly and sub-pixel emission variability (i.e., the aggregation error) in the error budget.

In this study, the prior uncertainty for each grid cell is defined as 150 % of the maximum value of the prior emissions among the eight nearest neighboring grid cells for the corresponding month. The scaling factor adopted here (150 %) is slightly higher than values used in previous studies (e.g., 120 %) (Cressot et al., 2014), in order to account for the higher spatial resolution and the limited number of emission inventories applied in this work. Four emission categories include total (sum of anthropogenic and natural sources), fire, wetlands, and anthropogenic CH₄ (data sources are listed in Table S1) (van der Werf et al., 2025, 2017; Kaiser et al., 2012; McDuffie et al., 2020; Crippa et al., 2024). The number of adopted inventories is limited (three datasets for fire and anthropogenic emissions, and four for wetlands, seen in Table S1). While this may influence the exact optimized configurations under the prescribed prior, it does not fundamentally affect the framework performance. As shown in Sect. 3.4, the test with spatially perturbed prior fields demonstrate that the framework adaptively adjusts site layouts in response to changes in prior spatial structure. All prior data are acquired for the year 2023, representing the most up-to-date ensemble of different emission inventories currently available. The reference year of the inventories therefore differs from that of the meteorology used for the transport simulations (2025). This temporal mismatch is not ideal, particularly for meteorology-sensitive natural sources such as wetlands and fires, and may affect the absolute uncertainty reductions or the placement of individual sites. However, because all candidate networks are evaluated consistently using the same prior and transport framework, the main relative spatial priorities and overall methodological conclusions are expected to remain broadly robust. All prior monthly emission fields are first regridded to a common 1° × 1° grid to ensure consistency with H and then the uncertainties are estimated. The prior error covariance matrix is constructed as: 2B=dCdT where d is a vector of gridded 1σ prior uncertainties, and C is a spatial correlation matrix. Spatial correlations Cij between grid cells i and j are represented using an exponential decay function: 3Cij=exp⁡-dijl where dij is the distance between grid cells i and j on the sphere. A land–sea mask is applied to prevent correlations between land and ocean grid cells, and a horizontal correlation length scale of 500 km is assumed over land and ocean. The sensitivity analyses to determine this value are detailed in Sect. 2.3. The resulting covariance matrix B is constructed separately for each target month and emission sector at 1° resolution. The resulting uncertainty budgets are comparable to those reported in previous studies (Fig. S1), as discussed in Sect. 2.3.

Transport sensitivities (H) are derived from adjoint simulations of the LMDZ model (Hourdin et al., 2020) in January and July 2025, run globally at approximately 90 km horizontal resolution using a hexagonal grid and 79 vertical layers. This relatively high resolution for a global transport model allows realistic representation of regional transport patterns while avoiding the need for lateral boundary conditions required by regional models. For simplicity, we assume that the observations are directly XCH₄, without any specific averaging kernel and associated retrieval prior profile. Chemical loss processes are neglected, as the analysis focuses on a within-month timescale. Flux sensitivities are reprojected onto the 1° grid within H using the adjoint of a mass-conserving flux interpolation, ensuring consistency between the inversion control vector and the sensitivity matrix. Details of the LMDZ hexagonal-grid simulations are provided in Chevallier et al. (2025). This model is run for full calendar months. In order to avoid running the adjoint over more than one calendar month at a time, we take only XCH₄ observations into account during the second half of the month. Thus, the sensitivity of the earliest observation of a month to surface fluxes from previous months is assumed to be sufficiently diluted so as not to significantly improve knowledge of African emissions. Observations at each site are simulated once per day at local noon, and the adjoint model is integrated backward to the first day of the same month, resulting in backward integration lengths ranging from 16 to 30 d depending on the month. Examples of site-specific footprint sensitivities are shown in Fig. S2. The posterior error covariance matrix A is given by: 4A=B-KHB and the relative reduction in uncertainty brought by these observations can be expressed as: 5I-AB-1=KH In this study, posterior uncertainty reduction relative to the prior is used as the primary metric to evaluate and compare different observation network configurations. It is important to note that the uncertainty reductions reported here should be interpreted as a proxy for the potential information gain achievable by an optimized network, rather than as a direct prediction of operational inversion performance. This is partly due to simplifying assumptions adopted for network design purposes, including the use of transport sensitivities derived from half-month adjoint integrations and prescribed, spatially uniform observation uncertainties.

Building on the Bayesian inversion framework described above, we develop a strategic Bayesian network design framework to optimize XCH₄ observation networks of new FTIR instruments beyond the existing six stations surrounding Africa and the three in Ivory Coast, Namibia, and shore of Lake Victoria. Among these operational sites, four (Ascension, Izaña, La Réunion, and Nicosia) belong to the TCCON network, which operates high-resolution FTIR spectrometers (typically Bruker Optik GmbH IFS 125HR FTS) (Pollard et al., 2021), whereas the remaining stations use lower-cost EM27/SUN instruments. Three of these stations (LAMTO, AMV, and Amsterdam Island) are operated by the Laboratory for Climate and Environmental Sciences (LSCE), one (Gobabeb) by the Karlsruhe Institute of Technology (KIT), and one (Jinja) by the University of Leicester (Table S2). The framework quantifies how posterior uncertainty in African CH₄ emissions responds to incremental network expansion and identifies an optimal balance between information gain and network size. The optimization assumes a predefined candidate site pool reflecting practical deployment constraints. For the African case study, the pool consists of nine existing stations, predominantly located along the continental periphery, four planned African sites outside the current operational network, and 21 additional candidate sites, yielding 34 potential locations in total (Table S2). The candidate locations were identified through consultation with project partners and selected to balance scientific relevance with preliminary deployment feasibility. Specifically, they were chosen to improve coverage of major African methane-emission regions, including areas with high prior emissions, while also considering the prospective availability of local institutional support and basic research infrastructure, such as universities, observatories, or field stations capable of hosting, operating, and maintaining an EM27/SUN instrument. Their inclusion in the candidate pool does not imply a confirmed deployment commitment, and final installation would require further site-specific logistical and technical assessment. The nine operational and four planned African sites are treated as a fixed baseline network, while the remaining candidate sites are considered for incremental expansion. The framework simultaneously determines the optimal number of additional observation sites based on uncertainty-reduction efficiency and identifies the spatial configuration of sites that minimizes posterior uncertainty at the prescribed network size using Bayesian evaluation.

This system first quantifies how posterior uncertainty in spatially integrated African CH₄ emissions decreases as additional observation sites are introduced, with the goal of determining an efficient network size prior to optimizing the exact site locations. Let x∈RN denote the gridded emission state vector. The target quantity is defined as a linear functional of the state: 6y=lTx where l is an aggregation vector (i.e., grid emissions in Africa). The corresponding prior uncertainty is obtained by applying this operator to the prior covariance B: 7σprior2=lTBl For a given network configuration c, we construct the observation operator Hc by stacking all available daily column sensitivities from the base network plus the selected candidate sites after cloud filtering, and compute the posterior covariance Ac following the Bayesian update described in Sect. 2.1, 8Ac=B-BHcT(HcBHcT+R)-1HcB The posterior uncertainty of the same aggregated quantity is then estimated: 9σpost2=lTAcl We then quantify the information gain for configuration c using the relative uncertainty reduction r(c): 10r(c)=1-σpost(c)σprior For each candidate number of additional site n, we evaluate an ensemble of configurations formed by combining the fixed base network with all (exhaustively enumerated) n-site subsets from the candidate pool. This yields an ensemble of σpost(c) and thus r(c) values that reflects both transport-sensitivity overlap and cloud-driven data availability constraints. The ensemble-mean uncertainty reduction at network size n is denoted as P(n): 11P(n)=1Cn∑c∈Cn1-σpost(c)σprior

We summarize network-size performance by the ensemble-mean reduction. The optimal number of additional sites n* is determined using a diminishing-return criterion: n* is the smallest n for which the relative marginal gain (ΔP(n)=(P(n)-P(n-1))/P(n-1)) falls below a prescribed threshold ϵ=0.6 %, corresponding to a 0.6 % additional reduction per added site (sensitivity tests shown in Sect. 3.4).

Given the optimal network size n*, the optimal configuration is selected from the ensemble of configurations with n=n* as the one that provides the largest uncertainty reduction in total African CH₄ emissions. Sector-specific uncertainty reductions are subsequently evaluated by applying sectoral prior covariance matrices B, while retaining the same transport sensitivities H. Differences in uncertainty reduction across sectors therefore primarily reflect contrasts in prior uncertainty structures rather than transport sensitivities.

The horizontal correlation length determines how prior emission errors are spatially coupled in the covariance matrix B. In simple terms, it controls how strongly emission errors in one grid cell are assumed to be correlated with those in neighboring cells. A larger correlation length implies that flux corrections inferred at one location can spread over a broader surrounding region, effectively distributing observational information across larger spatial scales. This generally leads to more optimistic large-scale uncertainty reduction, whereas shorter correlation lengths confine corrections to local scales and yield more conservative reductions. To assess the sensitivity of our results to this assumption, we conducted experiments with correlation lengths ranging from no spatial correlation to 1000 km (Fig. 2). Posterior uncertainty reduction increases substantially with larger correlation lengths. For example, the reduction achieved by the existing nine operational sites rises from 18 % under no correlation to 76 % at 1000 km. This increase is nonlinear and gradually saturates, with a clear flattening beyond approximately 500 km. We therefore adopt 500 km as the default value, representing a pragmatic compromise between local and large-scale coupling. Under this assumption, the resulting global prior uncertainty budget is approximately 88 Tg yr⁻¹ (∼ 17 %) (Fig. S1), which is close to the ∼ 18 % global uncertainty reported by Saunois et al. (2025). Regional uncertainty budgets over Africa are estimated to range between 33 % and 50 %, which fall within, though slightly below, the broader range of 31 %–90 %. These comparisons suggest that the magnitude of the prescribed prior uncertainties is broadly consistent with current global methane budget assessments.

At present, the lack of dense biogeochemical in situ flux observations over Africa prevents an empirical constraint on spatial error correlations. The adopted length scale should thus be regarded as a structural assumption rather than a directly observed quantity. Given the strong spatial heterogeneity of wetland emissions, true correlations likely vary across regions and seasons. While the assumed correlation length substantially affects the absolute magnitude of posterior uncertainty reduction, it has limited influence on the relative ranking of network configurations. The incremental gains from adding new sites remain consistent across the tested range, indicating that the optimization results are robust to reasonable variations in this parameter.

Cloud conditions strongly influence the effectiveness of ground-based XCH₄ observations by limiting both data availability and the sensitivity of column observations to surface emissions. Cloud cover reduces the number of valid retrievals and weakens the effective constraint that individual stations can provide on surface fluxes (Choudhury and Goren, 2025). To explicitly account for this effect, cloud screening is directly incorporated into the construction of the observational sensitivity matrix H. Hourly total cloud cover (TCC) fields from the fifth generation ECMWF reanalysis for the global climate and weather (ERA5) (Hersbach et al., 2020) are used for January and July 2025. For each baseline and candidate observation site, cloud fraction is extracted from the nearest ERA5 grid cell. Daily cloud conditions are derived from hourly cloud-fraction data between 08:00 and 18:00 local time, corresponding to the typical daytime observation window of the EM27/SUN spectrometer (Frey et al., 2019). Under the default settings, a day is classified as cloud-contaminated and excluded if more than 10 % of the hourly records (maximum cloudy-hour fraction, MF in Table S3) have a cloud fraction (CF) greater than 0.5. This conservative screening is applied to the latter 15 d of each month, corresponding to the period over which transport footprints are simulated. Only days passing the cloud filter are retained, and their corresponding footprints are included as individual rows in the sensitivity matrix H. Cloud-contaminated days are excluded entirely, effectively reducing the number of observational constraints associated with a given station.

Cloud screening affects the inversion by modifying the effective sensitivity matrix H. By reducing the number of valid observations and altering their temporal sampling, cloud filtering decreases the available information content and limits the achievable posterior uncertainty reduction for individual sites. Embedding cloud screening directly into the construction of H therefore allows the framework to account for more realistic observational availability and prevents overestimation of the constraint provided by candidate stations. This treatment also contributes to the diminishing marginal returns observed when adding sites in regions with frequent cloud cover, ensuring that the optimized network design reflects both atmospheric transport sensitivity and practical observing conditions. To assess the robustness of the network design, sensitivity experiments are conducted by varying key cloud-related parameters, together with additional tests of other major system parameters (18 experiments in total; see Sect. 3.4).

African CH₄ emissions exhibit strong spatial heterogeneity across sectors, with anthropogenic and wetland sources dominating the continental total and fire emissions contributing more episodically and regionally (Figs.  3 and S3). In January, anthropogenic sources account for 57.9 % of total African CH₄ emissions, followed by wetland (31.5 %) and fire (10.6 %). In July, the corresponding contributions are 52.6 %, 32.3 %, and 15.1 %, respectively (Fig. S4). Anthropogenic emissions exhibit a relatively stable spatial pattern across months, with pronounced hotspots over the Gulf of Guinea, the Nile Delta, and parts of South Africa, reflecting a spatially fragmented and regionally clustered structure (Mostefaoui et al., 2024). Wetland emissions show broadly similar mean spatial patterns in both months, with strong clustering over Central Africa, particularly around the Cuvette Centrale peatland complex in the Congo Basin, a well-recognized hotspot of tropical CH₄ emissions (Lunt et al., 2019; Barthel et al., 2022; Xiao et al., 2024). In contrast, fire emissions display pronounced seasonal shifts, concentrating mainly in southern Africa in July and in Central Africa in January, consistent with previous studies (van der Velde et al., 2024; Eames et al., 2025). Across the inventories adopted as priors in this study, biogenic sources exhibit substantially greater variability despite the limited number of available inventories. Fire and wetland CH₄ emissions show mean coefficients of variation (CV) of 84 % and 127 %, respectively, whereas anthropogenic emissions exhibit a much smaller CV of 22 % (Fig. S5). This pronounced inter-inventory spread underscores the considerable uncertainty associated with biogenic sources and highlights the need for improved observational constraints, particularly for Africa where natural sources contribute a substantial fraction of total methane emissions.

Against this emission context, we first quantify the constraint provided by the existing observing network. The nine operational sites alone (Fig. 3a) reduce the posterior uncertainty of total African CH₄ emissions by 62 % in January and 64 % in July (Fig. S6). It is important to note that the absolute magnitude of posterior uncertainty reduction depends on prior error assumptions (Fig. 2) and should therefore be interpreted primarily as a comparative reference metric. The substantial reduction obtained from only nine sites thus reflects posterior covariance changes under assumed error structures rather than real-world inversion accuracy. Incorporating the four planned African EM27/SUN sites (Yangambi, Mbandaka, Nouabalé-Ndoki, and Spioenkop) outside the current operational network (dots in Fig. 3b) yields marginal additional reductions, reaching 63 % in January and 65 % in July (Fig. S6). Three of these stations are located within the Congo Basin region, forming a dense cluster in Central Africa, while the fourth is situated in southern Africa. The three central African sites therefore sample broadly similar emission regions. In addition, regional wind fields organize coherent transport pathways across the Congo Basin, while high convective available potential energy (CAPE) promotes strong vertical mixing (Fig. S7). Together, these atmospheric conditions lead nearby stations to experience similar upwind sensitivities, resulting in substantial overlap in transport footprints (Fig. S2b and d).

To assess the upper bound of the achievable constraints, we consider an idealized scenario in which all candidate sites are simultaneously deployed. Under this configuration, uncertainty reduction reaches 71 % and 73 % in January and July, respectively (Fig. S6), yet the improvement relative to the current network is clearly sublinear (see Sect. 3.2). As site density increases, transport footprints increasingly overlap (Fig. S2), particularly along dominant seasonal flow structures such as the cross-equatorial pathway in January and the West African monsoon corridor in July (Fig. S7). These organized circulation regimes channel air masses through similar regions, causing additional sites to sample correlated source areas and thereby limiting incremental information gain. Cloud-related data loss further constrains the effectiveness of the network to constrain emissions within the convective Intertropical Convergence Zone (ITCZ), including the southern Congo Basin in January and the Sahelian belt in July (Fig. S7). Together, these results demonstrate that simply increasing the number of observation sites does not guarantee proportional improvements in CH₄ emission constraints. Instead, the strong nonlinearity between network size and uncertainty reduction underscores the need to jointly optimize both the number of additional sites and their spatial configuration to achieve cost-effective network design.

As the number of observation sites increases, the uncertainty reduction exhibits a clear diminishing-return behavior across all emission sectors (Fig. 4). For both total and sectoral CH₄ emissions, the ensemble-mean uncertainty reduction P(n) increases when a small number of sites are added, but progressively saturates as additional sites provide increasingly redundant information due to overlapping transport sensitivities. Correspondingly, the relative marginal gain ΔP(n) decreases monotonically with increasing network size, providing an objective criterion for identifying an optimal number of new stations. This behavior is consistently observed for total, fire, wetland, and anthropogenic emissions, confirming that diminishing returns are an intrinsic feature of network expansion rather than an artifact of sector-specific prior assumptions. It is important to note that the sector-specific experiments vary only the prior covariance (B), with identical transport sensitivities (H), and are designed to diagnose how source heterogeneity affects network-size requirements, rather than to imply perfect sector separability in real-world inversions, where sources are spatially mixed and attribution remains prior-dependent.

Despite this common pattern, the optimal number of additional sites required to satisfy the marginal gain criterion (ϵ=0.6 % in default setting) varies across sectors and between months (Fig. 4), reflecting differences in the spatial heterogeneity and seasonal redistribution of emission sources, as well as in atmospheric transport patterns. Fire emissions require the fewest additional sites, with a single new site sufficient in January and July, respectively, to reach the threshold. This reflects the strong spatial clustering of African fire activity, concentrated in the Sahel–Sudan belt during boreal winter and in the southern miombo woodlands and savannas during boreal summer, which are already well covered by the four planned stations (Figs. 4b and S3b). Wetland emissions require 11 new sites in January and 10 in July. Although their mean emissions are strongly concentrated over Central Africa, seasonal variability extends across large parts of the continent, with increases and decreases spanning both northern and southern Africa (Fig. S8c). Capturing this widespread variability therefore requires a larger number of observing sites. In contrast, anthropogenic emissions exhibit a more spatially dispersed distribution across the continent (Fig. S3d), resulting in the highest demand for additional observation sites. To satisfy the same marginal gain criterion, 21 new sites are required in both January and July. Notably, this value corresponds to the upper limit of the candidate pool, and the marginal gain criterion is not fully satisfied in the January case, suggesting that the true optimal network size for anthropogenic emissions likely exceeds the currently available candidate locations.

As an aggregate of sectoral contributions, the optimal number of additional sites for total CH₄ emissions falls between those of the source sectors, yielding optimal values of 7 in January and 10 in July. For the subsequent configuration optimization, we adopt the July-derived optimal site number (10 sites) as the target network size. This choice is motivated by the fact that July represents a season with systematically higher CH₄ emissions across most sectors except for anthropogenic sources (Fig. S4), implying stronger atmospheric signals and enhanced spatial overlap among source influences. Designing the network under this more emission-intensive scenario provides a stringent and practically relevant benchmark, ensuring that the selected configuration remains effective during periods of elevated emissions.

We next examine the spatial configuration of observation sites under the optimized network size and assess its effectiveness in constraining total and sectoral CH₄ emissions. Figure 5 shows the spatial distribution of uncertainty reduction for total, fire, wetland, and anthropogenic CH₄ emissions in July, obtained using the optimal 10-site configuration (January results are shown in Fig. S9). The optimized configuration is selected as the best-performing solution among all candidate site combinations in the ensemble, ensuring comprehensive and robust exploration of the configuration space (Fig. S10).

The ten sites contributing most strongly to the total uncertainty reduction are Nile, Tamanrasset, Arta, Kigali, Bujumbura, DaresSalam, Kalene, Maun, Wits, and Kimberley (closed black circles in Figs. 5 and S9). This configuration reduces the posterior uncertainty of total African CH₄ emissions by 69 % in January and 73 % in July. These values are close to the 71 % and 73 % reductions achieved in January and July, respectively, under the idealized scenario in which all 34 sites are deployed (Sect. 3.1). This comparison demonstrates that the majority of the attainable information gain can be captured by a carefully optimized subset of sites, without resorting to a uniformly dense and substantially more costly network. At the sectoral level, the optimized configuration achieves uncertainty reductions of 91 % and 94 % for fire emissions, 87 % and 84 % for wetland emissions, and 68 % and 65 % for anthropogenic emissions in January and July, respectively. Overall, more than 65 % uncertainty reduction is attained across all sectors with only ten additional stations, highlighting the efficiency of the optimized network design.

The spatial arrangement of the selected sites reveals a deliberately dispersed and complementary network across the African continent, designed to balance source-region coverage and inter-site spacing while minimizing redundant transport sensitivities. In northern Africa, the inclusion of site Nile and Tamanrasset substantially enhance sensitivity to anthropogenic CH₄ emissions associated with irrigated croplands and densely populated regions, which are weakly constrained by the existing observing network. Across equatorial Africa, sites such as Arta, Kigali, Bujumbura, DaresSalam, and Kalene are distributed along a north–south corridor spanning the Congo Basin and its surroundings. This alignment closely follows the core wetland CH₄ emission hotspots while maintaining sufficient separation from existing and planned stations, thereby reducing footprint overlap and maximizing the marginal information gain of each site. In southern Africa, the combination of Maun, Wits, and Kimberley strengthens constraints across multiple sectors simultaneously, improving sensitivity to wetland emissions in the Okavango region as well as to fire and anthropogenic emissions over southern Africa. Although the optimized sites are all located within Africa, their impact on uncertainty reduction is not confined to the continent. Owing to large-scale atmospheric transport, secondary uncertainty reductions extend into adjacent regions such as the Middle East and parts of South Asia (Fig. 5), providing an additional benefit of the optimized African observing network beyond its primary target region.

We evaluate the robustness and practical applicability of the optimized network using three complementary analyses based on the July total CH₄ emission case, which represents the most emission-intensive season (Fig. S4): sensitivity tests to key assumptions, ranking of candidate sites under the default setting, and a randomly perturbed-prior experiment (Fig. 6).

Sensitivity experiments explore variations in observational uncertainty, cloud-related constraints, and major system parameters (Table S4), examining both the optimal number of additional sites and the corresponding best configurations (Fig. 6a). Across the 18 tests, the optimal site number shows clear dependence on assumptions that control effective observational coverage. In particular, cloud-related parameters exert the strongest influence. Stricter cloud screening, implemented through lower cloud fraction thresholds (i.e., less data available during cloudy periods) or more restrictive maximum allowable cloudy-hour fraction (i.e., a larger required fraction of cloud-free hours) requirements, reduces data availability and increases the number of sites required to satisfy the marginal gain criterion (ϵ). The optimal number of additional sites increases to 13 when the maximum cloudy-hour fraction is set to zero (MF0) and up to 19 when the cloud fraction threshold is reduced below 0.3. Footprint integration length shows a similar effect: as the window decreases from 25 (Int25) to 10 (Int10) days, the optimal network size increases from 11 to 21 sites, reflecting the need for denser spatial sampling when long-range sensitivity is reduced. In contrast, the spatial configuration of selected sites remains highly consistent. The default ten-site solution (Nile, Tamanrasset, Arta, Kigali, Bujumbura, DaresSalam, Kalene, Maun, Wits, and Kimberley) is repeatedly recovered across tests, indicating that once network size is prescribed, the optimization converges toward a stable core set of locations that provide complementary and nonredundant information.

Beyond identifying a single optimal configuration, the framework also provides a quantitative prioritization of candidate sites. Under the default parameter setting, optimization is repeated for prescribed network sizes ranging from 1 to 21 additional sites, and the selection frequency of each site is recorded (Fig. 6b). Sites selected more frequently can be interpreted as having higher priority in sequential network expansion. Notably, the top ten ranked sites correspond exactly to the ten-site optimal configuration, demonstrating internal consistency of the framework. A complementary sequential-growth experiment, in which one site is added at each step to maximize the additional uncertainty reduction conditional on the previously selected network, identifies the same ten sites in the same order (Fig. S12). This agreement further demonstrates the robustness of the site ranking across alternative deployment strategies. The framework can therefore support a practical, prioritized rollout when the number of new stations is constrained by budget or logistics.

To assess dependence on the assumed prior emission distribution, we further conduct a randomly perturbed-prior experiment in which July CH₄ emissions are spatially shifted and rescaled, generating modified hotspot patterns (Figs. 6c and S11). The optimized configuration derived under the perturbed prior retains the overall spatial structure of the base solution but exhibits targeted adjustments. Specifically, Kigali is replaced by Dahra, reflecting enhanced sensitivity to regions where emissions increase under the perturbed prior without sufficient observational constraint. The associated transport footprints confirm that these newly selected sites better capture the redistributed emission signals. This adaptive response indicates that the optimization is not rigidly tied to a fixed prior assumption; rather, site placement dynamically adjusts to changes in emission patterns while preserving the physically constrained backbone of the network.