NDMI: Normalized Difference Methane Index

• NDMI is defined on Sentinel-2’s SWIR bands to detect methane plumes by quantifying differential absorption and normalizing brightness variations.
• It integrates into deep learning models as a 13th channel, enhancing spatial attention and reducing false negatives with measurable metric improvements.
• NDMI’s formulation suppresses background noise and confounding illumination effects, making it essential for robust methane monitoring in varied landscapes.

The Normalized Difference Methane Index (NDMI) is a spectral index formulated to enhance the detection of methane plumes in multispectral satellite imagery. Defined using the shortwave infrared (SWIR) bands of Sentinel-2, NDMI exploits the differential methane absorption properties of these bands to produce a normalized index sensitive to methane’s characteristic atmospheric signatures. This index is instrumental in automated methane detection pipelines, particularly when integrated as an explicit feature within deep learning architectures that prioritize methane-relevant cues while suppressing background variability (Ahsan et al., 2 Dec 2025).

1. Mathematical Definition and Physical Rationale

The NDMI is mathematically defined on a per-pixel basis as

$$\mathrm{NDMI} = \frac{\rho_{B12} - \rho_{B11}}{\rho_{B12} + \rho_{B11}}$$

where $\rho_{B11}$ and $\rho_{B12}$ are the (top-of-atmosphere or surface) reflectances in Sentinel-2’s SWIR band 11 (1565–1655 nm) and band 12 (2100–2280 nm), respectively. The physical motivation derives from the pronounced methane absorption features in the SWIR—specifically, strong absorption occurring in the 2100–2500 nm region (covered by B12), whereas B11 lies in an “off-band” region with substantially weaker absorption.

By forming the difference $\rho_{B12} - \rho_{B11}$, NDMI highlights pixels where elevated methane absorption (e.g., a plume) depresses B12 significantly more than B11. Normalization by $(\rho_{B12}+\rho_{B11})$ compensates for brightness variations due to scene illumination or albedo, restricting the index to the $[-1, 1]$ interval and attenuating signals from confounding factors such as shadows or soil moisture (Ahsan et al., 2 Dec 2025).

2. Implementation on Sentinel-2 Imagery

NDMI computation follows a multi-stage remote-sensing workflow:

• Data Acquisition and Radiometric Calibration: Sentinel-2 L1C tiles are retrieved for target dates (using Sentinel Hub API), converted to surface reflectance (L2A) via Sen2Cor or equivalent.
• Resolution Harmonization: All bands, including B11 and B12, are resampled to 20 m to match SWIR’s native resolution.
• Patch Extraction: 128×128 pixel windows (~6.55 km²) are centered on annotated plume polygons or negative locations, extracted with geometric alignment; random rotations are applied for training/validation splits.
• NDMI Calculation: For each pixel,

$$\mathrm{NDMI}_{i,j} = \frac{R^{B12}_{i,j} - R^{B11}_{i,j}}{R^{B12}_{i,j} + R^{B11}_{i,j}}$$

yielding a single-channel array with values in $(-1, +1)$.

• Channel Stacking and Standardization: The 12 original Sentinel-2 bands are concatenated with the NDMI to yield a 13-channel $(13, 128, 128)$ tensor. Each channel (including NDMI) is standardized: subtract mean and divide by standard deviation over the training set.

No explicit NDMI thresholding is used at this stage; the end-to-end model is trained to appropriately interpret both negative and positive NDMI responses (Ahsan et al., 2 Dec 2025).

3. Fusion of NDMI in Deep Learning Architectures

NDMI is integrated as an explicit input feature within AttMetNet, an attention-enhanced U-Net:

• Input-Level Fusion: The NDMI serves as the 13th channel alongside the 12 Sentinel-2 bands.
• Attention Mechanisms: The architecture introduces gated attention blocks at each encoder–decoder skip connection. These blocks use $1\times1$ convolutions to modulate encoder features $x$ and gating signals $g$ (decoder-side), followed by a scalar attention map generated via nonlinearities (ReLU, sigmoid). The NDMI-informed activations are broadcast and applied multiplicatively:

$x' = x \odot \alpha$

where $\alpha$ is the learned spatial attention mask. This mechanism prioritizes features spatially associated with high NDMI, facilitating selective amplification of methane-sensitive regions.

After initial fusion, decoder pathways combine the NDMI-guided skip connections with upsampled features, further processed through convolutional layers (Ahsan et al., 2 Dec 2025).

4. Training Impact and Model Optimization

The presence of the NDMI channel exerts a strong influence during model training:

• Informative Hinting: Providing NDMI as a precomputed spectral feature biases the learning process, reducing reliance on generic convolutional filters for identifying methane plumes.
• Class Imbalance Mitigation: Use of focal loss (α=0.75, γ=2) ensures that the model assigns more weight to rare, high-NDMI plume pixels, addressing severe positive/negative sample imbalance typical in methane datasets.
• Feature Localization: Grad-CAM ablation reveals that models utilizing NDMI achieve more spatially compact activations tightly co-localized with ground-truth plumes, as opposed to diffuse, non-specific responses in NDMI-absent models.

No hand-crafted post-processing on NDMI is utilized. After inference, a 90-pixel minimum-area filter is applied to declare scene-level plume positives in the binary mask predictions (Ahsan et al., 2 Dec 2025).

5. Quantitative Evaluation and Ablation

Ablation studies quantify the effect of NDMI across several metrics:

Model Variant	Bands (+NDMI)	Focal Loss	Balanced Acc	mIoU	Scene F1	FNR
MultiResUnet	12	No	0.81	0.64	–	–
MultiResUnet+	13 (NDMI)	Yes	0.85	0.65	–	–
AttMetNet (12ch)	12	Yes	0.83	0.63	~0.79	~0.24
AttMetNet (13ch)	12+NDMI	Yes	0.88	0.66	0.85	0.12

In Grad-CAM assessments, NDMI markedly sharpens spatial attention, reducing false negatives by ~20% in typical cases, and consistently boosts pixel- and scene-level metrics (e.g., +6 percentage points in F1, -12 points in FNR) (Ahsan et al., 2 Dec 2025).

6. Suppression of Background and Robustness

NDMI’s normalization mechanism suppresses confounding influences due to illumination, surface type, and atmospheric variability. As no further thresholding is required, the deep model learns an optimal mapping from raw and standardized NDMI (and other spectral bands) to segmentation outputs. The attention-enhanced integration focuses the architecture’s capacity on morphologically diffuse and irregular plumes that would otherwise evade conventional thresholding or naive band ratio methods (Ahsan et al., 2 Dec 2025).

7. Significance in Methane Remote Sensing and Deep Learning

The NDMI provides a physically grounded, application-specific spectral cue for methane detection in the context of Sentinel-2 SWIR data. Its fusion as an additional input channel to architectures such as AttMetNet directly addresses the challenge of simultaneous sensitivity (recall) and specificity (precision) in heterogeneous landscapes. Through joint exploitation with learnable attention mechanisms and optimized loss functions, NDMI enables robust, low-false-positive identification of methane events, supporting operational satellite-based greenhouse gas monitoring frameworks (Ahsan et al., 2 Dec 2025).