Plume vetting — a spectral test for matched-filter candidates

Plume vetting¶

A matched filter scores each pixel by one projection of its spectrum onto methane’s target, so anything that removes light under methane’s 2.3 μm band scores: carbonate and clay soils, salt pans, dark water, shadows, striping. A segmentation network on the matched-filter map learns plume shapes, which a plume-shaped confounder also has. Plume vetting (Xiang et al. ^[1]; Růžička et al. ^[2]) goes back to the radiances behind a candidate. It pairs the candidate’s strongest pixels with pixels outside it that have the same surface, divides them, and asks whether the ratio has the shape of methane’s transmittance. EMIT’s daily methane digest alerts without review when the misfit score $D_{\text{norm}}$ is below 0.3.

The work splits along a package boundary, “radiative transfer does not know about plumes”. radtrax answers a question about spectra: given two sets of pixels, how similar is the ratio of their paired mean radiances to a gas’s transmittance? It returns the fitted column $\widehat{\Delta X}$ and $D_{\text{norm}}$, and knows nothing of candidates. plumax answers the questions about plume objects: which of a candidate’s pixels are in (the seeds) and which are out (the background pool), how this scene’s clutter scores in the candidate’s shape (the null), and what to decide.

Vetting is a second test on the same data, not an independent one: its pixels are chosen by the matched filter and come from the same cube. It is more selective because it tests the shape of the absorption across a window of bands, where the matched filter tests one projection.

1. The test plumax runs¶

For in-pixels $I$ and out-pixels $O$ of one radiance cube, radtrax pairs them one to one on the bands the gas does not absorb, keeps the best-matched half, and divides the pairs’ mean radiances into a ratio spectrum $R(\lambda) \approx \eta(\lambda) E(\lambda; \Delta X)$, with $\eta$ the ratio of the paired surfaces and $E$ the gas’s band transmittance from radtrax’s forward model. It fits $R$ with a Legendre continuum times $E$, profiling over a grid of $\Delta X$ refined between its nodes, and scores the fit with Xiang et al.'s eq. 11, $D_{\text{norm}}$: 0 for a perfect fit, about 1 when nothing gas-shaped is left. The derivations, the curve of growth and the reasons for each setting are on radtrax’s absorption-shape test page.

Everything below is how plumax chooses $I$ and $O$ from a candidate, and what it does with the scores.

2. Seeds and the background pool¶

Write $M$ for the candidate’s pixels with a finite matched-filter score $\widehat{\Delta X}_{\text{MF}}$, and $q$ for the score’s 99th percentile over $M$. The seeds are the $k = 40$ strongest pixels of $M$ at or below the cap, grown by one pixel inside $M$ (select_seeds):

with $\oplus\, 3{\times}3$ one binary dilation by the 3 × 3 square and $g = 1$. The background pool is every pixel within a box of $b$ pixels around the seeds’ bounding box, outside every candidate $M_c$ of the scene, with a small matched-filter score (background_pool):

with $\tau_{\text{bg}}$ the window’s mf_background_mol_m2 (30 ppm·m for EMIT’s CH₄ window) and $b = 200$. So $I \subseteq M$, $O \cap I = \emptyset$ and $O \cap M_c = \emptyset$ for every candidate. These are the reference package’s settings ^[3], pv/config/config.yaml; the two sets then go to radtrax’s pairing as flat pixel indices.

3. A null from the same scene¶

The honest null is this scene’s clutter with no plume. Vet $S$ copies $M_s$ of the mask, each rotated and translated to where there is no candidate (null_masks), exactly as the candidate was vetted, and report (null_pvalue)

over the $S'$ copies with a finite score. $D_{\text{norm}}$'s threshold depends on the band set, the continuum’s degree and the ratio’s noise, so $\hat p$ travels between sensors where 0.3 does not.

Each copy draws an angle $\theta \sim U[0°, 360°)$ and rotates $M$ about the image centre (nearest neighbour); a rotation that keeps fewer than 90 % of the pixels is discarded. Among the integer shifts $\Delta$ that keep the rotated mask $M_\theta$ inside the image, the free ones are those with

found exactly as the zeros of the correlation of the candidates with $M_\theta$’s bounding box; one free shift is drawn uniformly. Randomness comes only from the caller’s jax.random key, so the same key gives the same copies.

4. One candidate¶

vet_candidate runs the steps in their fixed order with the window’s band selection: the seeds (1) and the pool (2), radtrax’s pairing on the window’s pairing bands, the ratio on its fitting bands, the fit and $D_{\text{norm}}$. Its VettingResult carries $\widehat{\Delta X}$ in mol/m², $D_{\text{norm}}$, the number of pairs, the ratio and the fit (continuum $P$ and transmittance $E$, the spectra an analyst plots as $R/P$ against $E$), and the continuum-only residual at $\Delta X = 0$ beside the fit’s residual at $\widehat{\Delta X}$.

$\widehat{\Delta X}$ is the column of the mean transmittance over the pairs, not the mean column: $E$ is convex in $\Delta X$, so it sits below the mean of the truth over the seeds. It is a score, not a retrieval; the column for an emission rate comes from a per-pixel retrieval of the vetted plume.

5. One scene¶

The notebook builds a 64 × 64 EMIT-like scene: 30 bands outside methane’s band, 9 inside it (2296–2356 nm), three surface classes, noise at SNR 300. Candidate A is a methane plume; candidate B is a plume-shaped patch of a surface whose reflectance dips by 6 % at 2335 nm, as a carbonate’s does.

The matched filter scores B at twice A; vetting reverses the order. A’s column is 93 % of the truth over its kept pixels: about 3 points go to averaging transmittances, the rest to paired surfaces that do not match exactly. With a constant absorption coefficient A’s column would be 1,691 ppm·m. B’s $\hat p$ was 0.43 when the null rejected random shifts; exact placement (4) draws other copies and gives 0.45 (A’s is 0 either way).

6. The decision¶

plumax.vetting returns scores, not verdicts. Three rules are on the table (#158): a fixed cut on $D_{\text{norm}}$ (EMIT’s 0.3), which depends on the sensor’s bands and noise; the scene null’s $\hat p$ (3), which calibrates the score against this scene’s clutter; and a likelihood ratio between the fits with and without the gas, from VettingResult’s two residuals. Until #158 settles it, report $\hat p$ with every score.

7. What plumax computes¶

The radtrax names are in radtrax.retrieval.absorption (API, theory). plumax.vetting is an L1 module on arrays; the operator on carriers, plumax.geo.PlumeVetting, follows (#157).

8. Where plumax departs from the reference code¶

• Exactly $k$ seeds. The reference keeps every pixel at or above the $k$-th score, more than $k$ on ties; plumax takes the top $k$, breaking ties by the lower flat index.

• Non-finite scores. A pixel with a non-finite matched-filter score is never a seed and never in the pool, and growth stays inside $M$’s finite pixels.

• The null avoids every candidate. The reference package draws 100 rotated and translated copies that avoid only their own plume’s boundary, and records their scores without a decision; plumax’s copies avoid every candidate, the mask itself included, and $\hat p$ is returned with the scores.

• Exact placement. Rather than rejecting random shifts that hit a candidate (which needs about 90,000 attempts for candidate A’s 100 copies), plumax finds each angle’s free shifts exactly and draws one uniformly. Given its angle, a copy is uniform over the free places; rejection would weight angles by their fraction of free places.