the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Sep 2026
Suppressing False Enhancements in Spectroscopic Greenhouse Gas Retrievals with the Differential Matched Filter
Abstract. We introduce the Differential Matched Filter (DiffMF), a computationally efficient extension to the Matched Filter (MF) designed to distinguish genuine Greenhouse Gas (GHG) enhancements from false enhancements. Conventional MF retrievals are often plagued by high-magnitude false concentrations driven by surface or atmospheric features that mimic the target absorption. DiffMF exploits the inherent functional characteristics of wavelength-varying spectroscopic observations—specifically, the derivatives of the whitened target and observed spectrum with respect to wavelength—to address the numerical ambiguities at the source of these artifacts. We validate this approach on a dataset consisting of 900 EMIT scenes containing 389 expert labeled CH4 plumes and 5,763 "plume-like" false plume detections, and demonstrate that simple metrics derived from our DiffMF retrievals provide an effective means to discriminate real GHG-enhanced pixels from false enhancements, to reject of false positive plume detections, and to guide iterative refinement of background covariance estimates without compromising the broadly effective filtering capabilities provided by the conventional MF. We further present preliminary results extending DiffMF to the retrieval of other GHG species including CO2, NO2, and NH3. To facilitate adoption across imaging spectroscopy instruments, platforms, and applications, we provide a complete Python implementation for reproducibility.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-3851', Anonymous Referee #2, 05 Oct 2026
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AC1: 'Reply on RC1', Jake Lee, 20 Oct 2026
We thank the reviewer for their careful reading of our manuscript and their constructive comments. We are glad that the reviewer found the scale and cosine-similarity decomposition useful for interpreting false enhancements.
- Discussion of Xiang et al.
Thank you for this correction. We agree that "often by a human operator" mischaracterizes the method. The approach of Xiang et al. requires a delineated candidate plume, but that candidate can just as easily come from an automated detector as from a human analyst.
We also agree with the reviewer's view of how the two approaches relate. Both are motivated by the same limitation of the conventional MF: the retrieved concentration length alone cannot tell whether an enhancement actually has the spectral shape of the target gas absorption. The two methods differ in when they are applied in the plume detection workflow, and in their mathematical formalism. Xiang et al. vet candidate plumes after detection. Their method fits the aggregate transmittance of a delineated plume with a physical absorption model and computes statistics against randomly shifted, plume-shaped background regions. DiffMF, on the other hand, is a linear extension of the MF that reuses the same background statistics, and it suppresses false enhancements in the retrieval itself, before any detection is made. The approaches are therefore complementary and can be used in sequence: DiffMF retrievals first suppress false enhancements, a detector (human or automated) then identifies candidate plumes, and the method of Xiang et al. performs additional vetting on the remaining candidates. DiffMF was in part motivated by some of the challenges in deployment of Xiang et al. that stem both from the estimation happening after a candidate plume proposal, and from poorly defined continua depending on the surface type being examined.
We will revise the paragraph as follows (L52-56):
"Xiang et al. (2025) address false alarms by fitting the transmittance of candidate plumes with a physics-based model of methane absorption. By matching the precise shape of the target signature, this provides a more discriminative test than the linear matched filter."
- "However, the approach requires candidate plumes to have been labeled in advance, often by a human operator. And with all of these approaches, the final emission estimate remains sensitive to any statistical biases and numerical ambiguities in the underlying concentration field."
+ "However, the approach operates after detection, requiring candidate plumes to first be delineated by a human analyst or an automated detector (Růžička et al., 2026). It also relies on the successful continuum definition, which can be operationally challenging on an automated basis with widely varying surface types. Our proposed approach similarly exploits the shape of the target absorption features, but suppresses false enhancements within the retrieval itself, prior to detection, and the two approaches may be applied in sequence. With all of these approaches, however, the final emission estimate remains sensitive to any statistical biases and numerical ambiguities in the underlying concentration field."
- Possible interpretation in the logarithmic domain
Thank you for this thoughtful suggestion. Our radiance-domain target perturbation, t − μ = c ⊙ μ, is the first-order linearization of Beer-Lambert attenuation of the background radiance, μ ⊙ exp(αc) ≈ μ ⊙ (1 + αc). In the log domain this attenuation becomes additive, ln x ≈ ln μ + αc, so the target perturbation is simply the unit absorption spectrum c and no longer depends on the background radiance. This is the basis of the lognormal MF of Pei et al. (2023), which we currently cite in the Introduction and Section 3.3.
DiffMF can be derived from the lognormal MF in the same way. Equation 7 only requires a linear target model and the background mean and covariance, so the log-radiance pixel and c can be whitened using log-domain background statistics and then differentiated with respect to wavelength. We would expect DiffMF's core behavior to carry over: false enhancements that broadly overlap the target absorption window but misalign with its finer features should remain misaligned in the derivatives of the whitened log-domain vectors. However, we have not evaluated this formulation. Changing the domain would also change the background statistics and the whitening transform, as well as the behavior at high concentrations, where the lognormal MF reduces the underestimation inherent to the linearized MF. While we would find the comparison quite interesting in detail, we feel that it would take significant scope, and warrant a separate discussion. However, we do feel this is an interesting direction to pursue, and as such we include a derivation of the lognormal DiffMF in Appendix B. We also include the following text to highlight this area of interest at the end of Section 2.2 (after L148):
+ "We formulate DiffMF in the radiance domain for consistency with operational EMIT MF retrievals. Since Eq. 7 only requires a linear target model and background statistics, DiffMF can be similarly derived from the lognormal MF (Pei et al., 2023) by whitening and differentiating the log-radiance pixel and unit absorption spectrum c. We provide this definition and derivation in Appendix B."
We will also reference this formulation in the Discussion, following the sentence describing future work on quantification with higher-order DiffMF retrievals (L331):
"Future work should investigate whether higher-order DiffMF retrievals themselves can be reliably used for quantification, as the inclusion of false enhancements in the same emission rate quantification methods can cause errors in concentration integration, fetch length, and other parameters."
+ "A log-domain DiffMF formulation (Appendix B) may be particularly suitable for this purpose, as the lognormal MF reduces the underestimation of high-concentration enhancements arising from the linearized Beer-Lambert approximation (Pei et al., 2023)."
We agree that the proposed comparison of ln(L_false) − ln(L_background) with c across several false-positive surface types would be an informative diagnostic. To keep this manuscript focused on the radiance-domain formulation used in operational EMIT products, we will not add new figures or experiments in this revision. However, Figure 3 and Appendix Figure A5 currently show which spectral discrepancies the d = 1 and d = 2 derivatives emphasize for a representative plume and false enhancement pair from the same scene, and Figure 4 summarizes these effects across all 252 plume and false enhancement pairs. We see the log-domain diagnostic as a natural direction for future work.
- Clarification of color scales in figure captions
Thank you for pointing this out. We will clearly specify the units and colormap ranges in the captions of all retrieval maps. For example, we will add the following to the caption of Figure 1:
+ "Retrieved concentration lengths are shown in parts-per-million meters (ppm-m). Colormap ranges are computed separately for each scene and DiffMF order, symmetric about zero with limits at the 90th percentile, to emphasize background characteristics."
We will make a similar addition to Appendix Figure A2, add units to the caption of Figure 8, and add units and the fixed colormap range (±750 ppm-m) to the caption of Figure 7. For Figure 2, we will also note that the plume and false enhancement rows share colormap ranges:
+ "Retrieved concentration lengths are shown in parts-per-million meters (ppm-m). Colormap ranges are computed separately for each DiffMF order, symmetric about zero with limits at the 90th percentile, and are shared between the plume (top row) and false enhancement (bottom row) panels."
We thank the reviewer again; we believe the planned revisions address each of these points and have improved the clarity and positioning of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-3851-AC1
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AC1: 'Reply on RC1', Jake Lee, 20 Oct 2026
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RC2: 'Comment on egusphere-2026-3851', Anonymous Referee #1, 07 Oct 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3851/egusphere-2026-3851-RC2-supplement.pdf
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AC2: 'Reply on RC2', Jake Lee, 20 Oct 2026
We thank the reviewer for their careful reading of our manuscript and their constructive comments. We are glad that the reviewer found the motivation clear and the figures supportive of our key takeaways.
Introduction
> Beyond listing instruments, can the technology improvements for GHG spectroscopy mentioned in the first paragraph be succinctly summarized? A short synthesis would clarify why these particular instruments were included.
Thank you for this suggestion. We will revise the first paragraph to summarize the relevant technology improvements (L15-22):
- "This advancement is largely driven by significant improvements in sensor technology like the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) (Green et al., 1998), AVIRIS-NG (Hamlin et al., 2011), and the recently developed AVIRIS-3 (Green et al., 2022). Satellite observing platforms such as [...] provide global observations that support climate research and inform policy-making."
+ "This advancement is largely driven by significant improvements in the signal-to-noise ratio, spectral and spatial resolution, and calibration of airborne imaging spectrometers like the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) (Green et al., 1998), AVIRIS-NG (Hamlin et al., 2011), and the recently developed AVIRIS-3 (Green et al., 2022), which enabled the mapping of individual GHG point sources at facility scales. Satellite observing platforms such as [...] extend these capabilities to orbit, providing global observations that support climate research and inform policy-making."
> Are false enhancements distinct from false positives in a way that matters for this paper? It seemed at times these words were used interchangeably, then at other times distinctly.
Thank you for pointing out this ambiguity. The distinction does matter for this paper. Throughout the manuscript, we use "false enhancement" for a pixel-level retrieval error, where the retrieval estimates a high concentration length for a pixel that does not contain the target gas. We use "false positive" for a detection-level error, where a detector (human or automated) incorrectly identifies a region as a plume. False positive detections are typically caused by spatially contiguous false enhancements, but not every false enhancement leads to a false positive detection. Sections 3.1 and 3.3 operate on false enhancements, while Section 3.2 operates on false positive detections.
We will add an explicit definition where false enhancements are introduced (L30-32):
+ "Throughout this work, we distinguish false enhancements, which are pixel-level retrieval errors, from false positives, which are detection-level errors where a human or automated detector incorrectly identifies a region of false enhancements as a plume."
We will also revise the instances where these terms were used loosely:
- L52: "Xiang et al. (2025) address false ~alarms~ positives by fitting [...]"
- L62: "While this suppresses albedo-driven false ~positives~ enhancements [...]"
> FPs are not widespread, at least historically. So while the novel false enhancement filtering methods may not be "common", I think it should be emphasized that manual expert removal has been heavily relied on.
We agree. Historically, false positives in published plume products have been rare precisely because every candidate plume is vetted by domain experts. For example, the EMIT plume products are produced through a multi-stage review process with multiple independent reviewers. We will emphasize this at the beginning of the related work paragraph (L49-50):
- "Despite the widespread application of MF GHG retrievals in remote sensing, novel approaches to detect and suppress false enhancements are not common."
+ "Despite the widespread application of MF GHG retrievals in remote sensing, operational plume mapping efforts have relied heavily on manual expert review to identify and remove false positives (Thorpe et al., 2023; Brodrick et al., 2025; Schuit et al., 2023), and novel approaches to automatically detect and suppress false enhancements are not common."
Methods
> More detail is needed on the scenes included. How were they chosen, and what regions, topographies, and land covers do they span (urban, forested, etc.)? How might the choice of scenes affect the evaluation of the method? The introduction names clouds and dark vegetation as contributors to false enhancements, so were these well represented?
Thank you for raising this point. We agree that Section 2.3 relies too heavily on Bue et al. (2026), and we will summarize how the scenes were selected and what they represent directly in the manuscript.
The 252 scenes containing plumes are drawn from the EMIT VISIONS CH4 data set described in Bue et al. (2026). This dataset consists of high-SNR EMIT methane retrievals acquired globally between 2022 and 2024, whose plumes were identified, delineated, and approved by multiple independent reviewers, then publicly released through the EMIT VISIONS portal. As detailed in Bue et al. (2026, Suppl. Sections 2.4-2.6), every plume in a scene must be exhaustively labeled and identifiable with high confidence from the MF retrieval alone, and every remaining enhancement must be identifiable as either background or a false enhancement. These criteria allow us to treat any ML detection that does not overlap an expert-labeled plume as a false positive.
The remaining 648 scenes contain "plume-like" false positive ROIs detected by the ML model described in Bue et al. (2026), meaning that they contain false enhancements with sufficient magnitude and morphological similarity to real plumes to confuse the model. These scenes and ROIs were identified by deploying the ML model on globally distributed background scenes, then keeping the scenes with false positive detections. As a result, the composition of these scenes is determined by the presence of the phenomena DiffMF is designed to address, rather than by a predefined sampling of regions or land covers. Because our evaluation operates on the false positive ROIs rather than on entire scenes, surface types that rarely produce plume-like false enhancements are underrepresented by construction, and their absence does not bias the false positive rejection results. The retained scenes include common confusers such as dark vegetation, infrastructure, and exposed minerals. Clouds are not represented because the valid pixel mask removes cloud-contaminated pixels from all scenes.
We will also correct the number of false positive scenes, which was misreported in the submitted manuscript (L154):
"5,763 "plume like" false positive ROIs across 648 scenes."
We will add the following to the first paragraph of Section 2.3, before the sentence referring the reader to Bue et al. (2026) (L155):
+ "The plume scenes were drawn from the EMIT CH4 Plume Dataset (Thorpe et al., 2026, Thorpe et al., 2025) , which consists of high-SNR EMIT methane retrievals whose plumes were identified, delineated, and approved by multiple independent reviewers. Every plume in these scenes is exhaustively labeled, and every remaining enhancement is identifiable as either background or a false enhancement (Bue et al., 2026, Suppl. Sections 2.4-2.6); we therefore treat any detection that does not overlap an expert-labeled plume as a false positive. The false positive scenes were identified by deploying the "EMIT_v1" model on globally distributed EMIT scenes without expert-labeled plumes, then keeping the scenes that produced false positive detections. These scenes were therefore selected by the presence of plume-like false enhancements, such as those caused by dark vegetation, infrastructure, and exposed minerals, and provide a challenging test of false positive rejection."
Results & Figures
> Figure 1: This is the largest figure, yet the two scenes that do not contain boxes A and B are barely discussed. Please explain what the reader should take from them.
Thank you for pointing this out. The two additional scenes illustrate the same behavior as the first scene in different settings, as well as one limitation of DiffMF. We will add the following paragraph following the discussion of Figure 2 (after L184):
+ "The remaining scenes in Figure 1 illustrate similar behavior. In scene emit20230822t070014 (middle row), the DiffMF(d=0) retrieval contains numerous linear false enhancements along roads and other high-contrast surface features; these are suppressed in the DiffMF(d=1) and DiffMF(d=2) retrievals, while the plume is preserved. In scene emit20230614t102415 (bottom row), broad false enhancements surrounding the plume and along the river are similarly suppressed for d>0. However, the columnwise artifact intersecting the plume persists across all d. Columnwise artifacts originate from corrupted columnwise background statistics rather than the spectral shape of individual pixels, and are therefore not suppressed by DiffMF alone; we address them in Section 3.3."
> Figure 2: DiffMF is clearly powerful, but the road in panel B is hard to describe as "plume-like" or as needing DiffMF to filter out. Would a morphology assessment or an overlay with road infrastructure maps suffice here? A more plume-like example would be preferable if one is available. If this is the best illustrative example, please discuss whether it is practical to need a method like DiffMF for such cases.
Thank you for raising this point. We agree that a human expert would readily dismiss this road by visual inspection. However, this example was not hand-selected for visual effect. As described in Section 3.1, it is the pixel with the maximum MF enhancement outside of any expert-labeled plume in the scene, selected by the same systematic procedure applied to all 252 scenes in our spectral library. Its retrieved concentration length (4,421 ppm-m) is nearly identical to that of the plume pixel in the same scene (4,715 ppm-m). This is precisely the ambiguity that DiffMF is designed to resolve, and Figure 3 uses this pair to illustrate the spectral mechanism behind it. We also note that this example is distinct from the "plume-like" false positive detections evaluated in Section 3.2, which are spatially contiguous ROIs that an ML detector incorrectly identified as plumes. The 5,763 false positive ROIs in Section 3.2 provide the large-scale evaluation of more plume-like cases.
Morphological filtering and infrastructure masking have important limitations in practice. As shown in the top row of Figure 2, real plumes frequently originate at facilities directly adjacent to roads and infrastructure that themselves produce false enhancements. Infrastructure masks would therefore also reject or truncate genuine plumes. Plumes can also appear elongated and linear under high wind speeds, which limits morphology-based rejection. In addition, infrastructure databases are incomplete and inconsistently maintained at global scales, and they must be accurately co-registered with each observation. In contrast, DiffMF suppresses the road while preserving the adjacent plume, at the pixel level and using only the observed spectra.
We will clarify these points in the discussion of Figure 2 (L183-184):
+ "Although this linear false enhancement is readily identified by visual inspection, its retrieved concentration length is comparable to the true plume pixel, and road and rooftop materials are a common source of false positive detections in ML-based plume detectors. Additionally, as shown in the top row, such false enhancements frequently occur adjacent to real plumes at emitting facilities, where morphological filtering or infrastructure masking would also risk rejecting the plume."
Section 3.2 Rejecting False Positive Plume Detections
> This was the most convincingly worded section on the method's impact and relevance to AI plume detection systems. I believe some of these points merit being reiterated in the introduction. The abstract might be strengthened by a statement on impact and contribution. [...]
Thank you for this suggestion, we will reiterate this framing in both the abstract and the introduction.
In the abstract, we will add a statement on impact (L6-10):
- "We validate this approach on a dataset consisting of 900 EMIT scenes containing 389 expert labeled CH4 plumes and 5,763 "plume-like" false plume detections, and demonstrate that simple metrics derived from our DiffMF retrievals provide an effective means to discriminate real GHG-enhanced pixels from false enhancements, to reject of false positive plume detections, and to guide iterative refinement of background covariance estimates without compromising the broadly effective filtering capabilities provided by the conventional MF."
+ "We validate this approach on 900 EMIT scenes containing 389 expert-labeled CH4 plumes and 5,763 "plume-like" false positive detections from a machine learning plume detector. Simple metrics derived from DiffMF retrievals discriminate real GHG-enhanced pixels from false enhancements and guide iterative refinement of background covariance estimates, without compromising the broadly effective filtering capabilities of the conventional MF. Most notably, a DiffMF-based filter rejects 80% of false positive detections at 70% plume recall, compared to 30% recall for an MF-based filter at the same rejection rate, addressing a key bottleneck towards fully automated GHG plume monitoring."
In the introduction, we will add the following to the end of the second paragraph (L29):
+ "False enhancements frequently produce false positive plume detections, which must currently be identified and removed through labor-intensive visual inspection by domain experts. As data volumes grow, this manual review becomes a key bottleneck and a fundamental obstacle to fully automated, machine learning-driven plume monitoring systems (Bue et al., 2026; Růžička et al., 2026).”
> Batchu et al. (2026) and Reuland et al. (2026) also highlight the ML false positive problem and could be cited here or elsewhere. More generally, the reference list draws noticeably from the authors' own institution, and the authors could broaden it in revision.
Thank you for these suggestions. We will cite Batchu et al. (2026) and Brandt, Reuland, et al. (2026) at the beginning of Section 3.2 (L210-211):
+ "Fully automated operational deployments of machine learning-driven GHG plume monitoring systems are impeded by false positive detections (Bue et al., 2026; Růžička et al., 2026; Batchu et al., 2026), and independent single-blind evaluations report non-negligible false positive rates across both instruments and analysis teams (Brandt et al., 2026)."
We will also broaden our reference list to better represent the work of the broader community. In particular, we will add references to the following works:
- Introduction (instrument and plume mapping context): Guanter et al. (2021), mapping methane point emissions with PRISMA; El Abbadi et al. (2024), technological maturity of aircraft-based methane sensing, and Sherwin et al. (2023), single-blind validation of space-based detection and quantification
- Introduction (reliance on manual review) and Section 3.2 (automated detection and false positives): Schuit et al. (2023), automated detection of methane super-emitters with TROPOMI, which combines ML detection with manual review; Rouet-Leduc and Hulbert (2024), automated detection with Sentinel-2; Joyce et al. (2022); Groshenry et al. (2022); Kumar et al. (2023), MethaneMapper; Růžička et al. (2026), false positive filtering
- Section 3.3 (columnwise background statistics): Ayasse et al. (2023), columnwise and pixelwise methane retrievals for imaging spectrometers.
- Section 3.4 (other gas species): Borger et al. (2025), NO2 and CO2 plumes from EnMAP; Balasus et al. (2026), ammonia plume mapping with SWIR imaging spectroscopy; Růžička et al. (2026), NH3 and NO2 detections
We thank the reviewer again; the planned revisions should make the terminology, data description, and impact of DiffMF considerably clearer.
Citation: https://doi.org/10.5194/egusphere-2026-3851-AC2
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AC2: 'Reply on RC2', Jake Lee, 20 Oct 2026
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