PaperlayerView exact revision on arXiv

Source-linked AI summary

Meteorology-driven Causal Nowcasting of Fugitive Landfill Emissions Enables Proactive Public Health Response

Timothy C. Pearce, David J. T. Smith, Alec Dobney, Alessia Freddo

arXiv:2608.14254v1cs.CYcs.AIcs.LGphysics.ao-phphysics.geo-ph

TL;DR

Fugitive-emission monitoring is largely retrospective, leaving a need for earlier community-impact detection. The paper anchors CAIRN’s temporal receptive field to measured coupling timescales and finds that it outperforms an engineered benchmark on high-exposure metrics while producing fewer false alarms.

  • Problem

    Existing fugitive-emission monitoring systems primarily characterize community exposure retrospectively, after impacts have occurred.

    Source: Introduction · p. 2, Discussion · p. 12

  • Method

    The paper anchors CAIRN’s temporal receptive field to causally measured coupling timescales rather than relying on engineered temporal lags.

    Source: Discussion · p. 12

  • Results

    CAIRN led the engineered benchmark on every high-exposure metric while producing fewer false alarms, 612 against 626 across 8,040 timesteps.

    Source: Discussion · pp. 12–13

  • Takeaways & Limitations

    Encoding temporal structure through measured dynamics reduces reliance on site-specific feature engineering.

    Source: Discussion · p. 13

    The causal hierarchy is regime-specific and must be re-estimated rather than assumed when applying the approach at a new site.

    Source: Operational pathway and limitations · p. 60

Abstract

from arXiv · show

Fugitive emissions from waste sites increasingly expose communities to toxic and odorous gases, yet public-health responses remain largely retrospective, with episodes investigated only after residents have been exposed. Here we show that the meteorological drivers of elevated hydrogen sulphide (HS) at a long-monitored European landfill, and the timescales over which they act, can be identified directly from routine monitoring data. We introduce CAIRN (Causal-Anchored Inference for Receptor Nowcasting), a machine-learning framework whose internal memory is matched to these measured timescales: a fast component tracking hour-scale wind-borne transport and a slow component tracking multi-hour weather changes. Trained to predict gas measurements, CAIRN operates using only routine weather variables and the calendar, without hand-engineered features. Its behaviour is consistent with the identified transport mechanisms, and the framework transfers unchanged to a second monitoring station and to co-emitted methane. Combining four such nowcasters produces a site-level, tiered alert aligned with WHO odour guidance that closely reproduces the alert generated by a direct sensor network and tracks an independent record of community odour complaints. Weather-driven nowcasting can therefore estimate community impact as an emission episode unfolds, providing public-health authorities with a validated, graded trigger for intervention and enabling exposure to be reduced during events rather than after them.

Introduction · Results

The study develops CAIRN, a raw-meteorology nowcaster that captures multiscale meteorological controls on fugitive odour exposure and improves High-class discrimination over an engineered benchmark through learned temporal memory. It transfers across receptors and co-emitted methane and supports a four-channel operational alert aligned with concentration-based tiers and community complaints, while intermediate-tier performance and single-channel correlations limit interpretation.

Introduction

  • The work frames fugitive odour exposure as an environmental-justice problem inadequately addressed by retrospective intervention, and proposes data-derived causal modelling to connect meteorology with community protection.The paper identifies missing empirical meteorology–exposure links, multiscale structure and independent validation against community wellbeing as the central gaps.Source: Introduction · pp. 2–4

Causal hierarchy of meteorological drivers

  • Transfer entropy identified pressure, wind direction and wind speed as the main directed-information drivers across timescales, with six-hour temperature tendency providing the surviving thermal signal.Wind direction dominated through 6 h, pressure remained significant through 12 h, and no tested cell was significant at 24 or 48 h, although coarse-scale tests were underpowered.Source: Causal hierarchy of meteorological… · p. 5

Physics-anchored learnt nowcasting

  • CAIRN used only four raw meteorological channels and calendar inputs, with fast and slow state-space pathways anchored at one and six hours, respectively, and no engineered derivatives or lag features.The six-hour anchor achieved 0.57 ± 0.01 F1-High and outperformed every tested alternative, whereas removing the slow-lane bound reduced performance to 0.48 ± 0.01.Source: Physics-anchored learnt nowcasting · pp. 6–7
  • CAIRN reproduced the empirical nocturnal peak and broad source-sector response, with sector-profile correlation r = 0.93 and source-sector probability 0.291 versus 0.077 outside it.It also recovered physically interpretable responses to unprovided pressure and temperature tendencies, while its predicted peak sector was displaced by approximately 34°.Source: Physics-anchored learnt nowcasting · p. 8

Walk-forward performance and community-impact validation

  • F1-High was 0.533 for CAIRN versus 0.501 for engineered XGBoost, a +0.032 (+6.3%) gain, although paired weekly differences were not significant.Recall-High was 0.618 versus 0.575 and precision-High 0.468 versus 0.445, while calibration metrics generally favored the benchmark.Source: Walk-forward performance and… · p. 8
  • CAIRN detects 38 more High-class events than the benchmark while producing 14 fewer false alarms, with AUC 0.898 versus 0.877 across 8,040 timesteps.The gain persists in rolling 24-hour metrics, although the paired weekly difference is not significant and CAIRN leads in 8 of 13 weeks.Source: Walk-forward performance and… · p. 9
  • Against a memoryless raw-input floor, learned state-space memory recovers +0.073 pooled F1-High versus +0.040 for engineered features, with the ordering surviving jackknife analysis.False alarms fall monotonically across the three arms from 717 to 626 to 612; the architectural comparison is more stable than the endpoint benchmark comparison.Source: Walk-forward performance and… · p. 9
  • The unchanged architecture transfers to methane, with daily predicted High probabilities correlating with the H2S model at r = 0.777 and Brier-High score 0.0724.The near-unit slope supports transfer across concentration scales, but the comparison is cross-protocol and the two class labels are linear transforms derived from H2S boundaries.Source: Walk-forward performance and… · p. 9

Multi-site network tier alerting and public-health framing

  • The four-channel alert uses meteorology-only inputs, WHO-aligned 30-minute debouncing, and thresholds (0.15, 0.50, 0.92), but intermediate tiers remain weak.Tier 0 and Tier 3 achieve F1 = 0.91 and 0.57, whereas intermediate tiers achieve F1 ≈0.35; Tier 2 requires recalibration before statutory-nuisance confirmation.Source: Multi-site network tier alerting and… · pp. 10–11
  • κw = 0.709 agreement with concentration-based alert tiers exceeds the vote-count baseline by Δκw = +0.07, with significant paired-bootstrap improvement.The fused system achieves 79.4% strict accuracy, but κw is the appropriate chance-corrected measure because Tier 0 dominates; leave-one-week-out refitting gives κw = 0.703.Source: Multi-site network tier alerting and… · pp. 10–11
  • r = 0.729 between fused CAIRN tier and independent daily complaints exceeds naive stagnation meteorology by +0.255, supporting a multi-channel community-impact signal.The correlation is 0.721 after leave-one-week-out refitting, while the lagged cross-correlogram uniquely peaks at lag 0 and the spatial complaint gradient declines with distance from the landfill.Source: Multi-site network tier alerting and… · pp. 11–12

Discussion

The findings support shifting fugitive-emission response from retrospective, complaint-driven investigation toward anticipatory intervention using meteorology-derived receptor-scale exposure indicators. CAIRN’s causal design, independent validation, and tiered fusion connect modelled exposure with operational public-health response while retaining important training, forecasting, and transferability limitations.

Causal meteorological controls

  • Wind direction, wind speed, and atmospheric pressure were the dominant meteorological information pathways, with the hierarchy replicated across estimator settings, time periods, and independent analytical approaches.Pressure’s directed-information share increased with aggregation scale and peaked at 12 h, consistent with barometric pumping and subsidence-related dilution suppression, although source-rate effects are not excluded.Source: Discussion · p. 12

Model design and benchmarking

  • CAIRN’s causally aligned temporal receptive field outperformed anchors outside the significant pressure band, while removing the physical bound reduced F1-High by 0.04 on 10 of 13 folds.The model led the engineered benchmark on every high-exposure metric and produced 612 versus 626 false alarms across 8,040 timesteps.Source: Discussion · pp. 12–13

Independent community validation

  • The meteorology-only exposure probability co-varied with withheld complaint counts at r = 0.585 across 88 days, with the cross-correlation peaking at zero lag.This supports tracking a human-reported exposure endpoint at the time of occurrence, while the complaint record remains downstream of the same events as the sensor labels.Source: Discussion · p. 13

Limitations and future training

  • Training still depends on periodic receptor H2S monitoring, but the fused tier tracked complaints at r = 0.721 versus r = 0.793 for deterministic sensor ground truth under leave-one-week-out refitting.Complaint data may therefore provide a future supervisory signal, although the initial H2S target remains important for physical threshold anchoring and independent validation.Source: Discussion · p. 13

Operational exposure indicator

  • The fused tier reproduced sensor-derived exposure classifications with substantial agreement (κw = 0.709; 0.703 under leave-one-week-out refit) and closely tracked community complaints.The tiered scale aligns with the FIDOL/WHO odour-annoyance framework and integrates meteorologically trained channels into an operational decision framework.Source: Discussion · pp. 13–14

Public-health and policy implications

  • Real-time, tiered exposure indicators could support proportionate interventions targeted to meteorological conditions, locations, susceptible populations, and operational periods of elevated risk.Forecast-weather substitution could enable forward projection, but retention of predictive skill under forecast uncertainty and validation beyond landfill settings remain open questions.Source: Discussion · pp. 13–15

Methods

The study combines year-long multi-site monitoring, causal temporal analysis, and two nowcasting approaches to predict WHO-aligned H2S alerts from meteorology and calendar information. CAIRN uses causally anchored dual-timescale memory and is evaluated with leakage-controlled expanding-window validation.

Data and study sites

  • Monitoring covered three downwind stations and one relocating supplementary receptor at 15-minute resolution throughout 2024, with MMF9 serving as the principal modelling receptor.The dataset includes H2S, CH4, wind direction, wind speed, temperature, pressure, and finite-difference temperature tendency; analyses used post-calibration-adjustment 2024 data.Source: Data and study sites · p. 15

Environmental characterisation

  • Environmental characterisation combines wind-sector exceedance analysis, H2S–CH4 association tests, diurnal phase and profile analyses, sunrise composites, and meteorological regressions.The analyses use CPF roses, correlation and power-law methods, spike co-occurrence, hysteresis metrics, nonparametric tests, and OLS slope tests.Source: Environmental characterisation · pp. 15–16

Causal analysis

  • Multiscale transfer entropy tests directed nonlinear information flow from candidate drivers to H2S across ten temporal scales using surrogate testing and multiple-comparison correction.The 96-hour scale was not estimable; the coarsest estimable scale was 48 hours, and split-half analyses assessed hierarchy stability separately from estimator ablations.Source: Causal analysis · pp. 16–17

Ensemble classifier-tree seasonal nowcaster

  • Four quarterly XGBoost classifiers predict Low, Medium, and High H2S classes from 24 engineered causal and calendar features using expanding training windows and WHO thresholds.The classes are Low < 2, Medium 2–7, and High ≥7 µg m−3; a three-hour majority vote aligns predictions with the 30-minute WHO averaging convention.Source: Ensemble classifier-tree seasonal… · p. 17

CAIRN: structured state-space dual-pathway nowcaster

  • CAIRN uses a minimal sixteen-dimensional meteorological and calendar input and three width-128, state-size-256 S4D blocks over 96-hour sequences, with strictly causal fast and slow pathways.The fast lane covers sub-hour to few-hour timescales.Source: CAIRN: structured state-space… · p. 18

Walk-forward validation and metrics

  • Models are evaluated by weekly expanding-window walk-forward validation over 13 autumn blocks totaling 8,040 timesteps, with causal context reserves and training-only preprocessing.The protocol uses fresh models and scalers, inner temporal probes for early stopping, and pooled confusion counts for period-wide metrics.Source: Walk-forward validation and metrics · pp. 18–20

Cross-species CH4 nowcaster and complaint validation · Code availability

CAIRN was extended to co-emitted CH4 and evaluated against independent community odour complaints, while four nowcasters were fused into a meteorology-only, tiered alert system. The implementation, checkpoints, and reproducibility materials are publicly available, with complaint data withheld as personal data.

Cross-species CH4 nowcaster and complaint validation

  • The CH4 nowcaster used the same architecture and weekly walk-forward protocol as H2S, with class thresholds derived by regression as Low < 1.854, Medium 1.854–2.756, and High ≥ 2.756 ppm.The CH4 model retained the original checkpoint-selection rule and was not re-trained under the inner temporal probe, making its reported values optimistic to the extent quantified elsewhere.Source: Cross-species CH4 nowcaster and… · p. 20
  • Daily High-class probabilities for both species were correlated with an independent 88-day record of community odour complaints, using lagged Pearson correlations from −7 to +7 days with lag 0 as the primary endpoint.Complaint data were excluded from training and unavailable to the classifier at inference time.Source: Cross-species CH4 nowcaster and… · p. 20

Multi-site Bayesian alert-tier classifier

  • Four independently trained H2S and CH4 nowcasters at receptors MMF9 and MMF2 were fused into a 15-minute network-event probability and ordinal alert tier using only meteorology at inference.Each channel used a 0.5 High-probability threshold and asymmetric latching with 45-minute onset and 30-minute clearance.Source: Multi-site Bayesian alert-tier… · p. 20
  • The continuous posterior used calibrated channel-state likelihood ratios and was mapped by hard thresholding alone to four sequential ordinal tiers at cut-points 0.15, 0.50, and 0.92, with no raw-sensor override.A ±25% sensitivity analysis on the channel likelihood ratios produced a maximum |∆κw| of 0.009.Source: Multi-site Bayesian alert-tier… · p. 20
  • Alert performance was evaluated against a deterministic raw-concentration ground-truth tier using quadratic-weighted Cohen’s kappa on 8,536 shared 15-minute timesteps from the Jan–Mar 2025 walk-forward window.A hard vote-count baseline isolated the contribution of soft-evidence fusion, while confidence intervals used 1,000 24-hour block-bootstrap resamples.Source: Multi-site Bayesian alert-tier… · p. 21

Code availability

  • The released CAIRN implementation includes the dual-pathway model, thirteen weekly checkpoints per species, standardisation parameters, feature and labelling code, and an acceptance test suite reproducing reported predictions.The command-line prediction workflow regenerates the walk-forward results of Fig. 6 and Extended Data Table ED2 from released checkpoints.Source: Code availability · p. 21
  • The transfer-entropy estimator, gradient-boosted benchmark, and scripts for Figs. 1–7 are available from the corresponding author and will be deposited in the same archive on acceptance.A versioned snapshot with a persistent DOI will be deposited at Zenodo on acceptance.Source: Code availability · p. 21
  • Fig. 8 cannot be reproduced from the released data because the community complaint record is withheld as personal data, and it supplies no quantitative result in this work.The figure is described as a map of the record’s spatial distribution.Source: Code availability · p. 21

Data availability

The study releases the principal receptor’s 15-minute meteorological and gas-concentration record with its reference implementation, while community odour-complaint data remain unavailable publicly because they are personal regulatory-process data.

Released monitoring data

  • A single Parquet file releases 15-minute wind, temperature, pressure, H2S, and CH4 measurements from 1 September 2023 to 31 December 2024 at the principal receptor.The dataset accompanies the reference implementation and underlies the nowcasting results.Source: Data availability · p. 21

Unavailable complaint data

  • Community odour-complaint records are withheld as personal data, so complaint analyses in Figs. 6c–d, 7d–f, and 8 cannot be regenerated from the public release.Derived daily counts are available from the corresponding author on reasonable request, subject to applicable information-governance conditions.Source: Data availability · p. 21

Site identification

Funding acknowledgement

The study was part-funded by the NIHR Health Protection Research Unit in Chemical Threats and Hazards, with views belonging to the authors rather than necessarily the NIHR or the Department of Health and Social Care.

Funding acknowledgement

  • The study received partial funding from the NIHR Health Protection Research Unit in Chemical Threats and Hazards through grant NIHR207293.The grant supported T.C.P, D.J.T.S, A.D. and A.F.Source: Funding acknowledgement · p. 22

SUPPLEMENTARY INFORMATION

The Supplementary Information provides the paper’s extended quantitative, contextual, sensitivity, and procedural material, organized into Extended Data, six Notes, six Methods subsections, tables, and a figure. It documents the analyses, model specifications, validation procedures, and robustness checks supporting the main article.

Organization

  • The supplement separates peer-reviewed quantitative Extended Data tables from contextual, per-panel, sensitivity, and full-procedural Supplementary Information.Extended Data Tables ED1–ED3 support the main figures and Results, while Supplementary Information contains six Notes, six Methods subsections, nine Tables, and one Figure.Source: SUPPLEMENTARY INFORMATION · p. 47

Supplementary Notes

  • The six Supplementary Notes cover regulatory and public-health context, Fig. 1 quantitative detail, seasonal ALE interpretation, prior-literature comparison, and MSTE-ablation robustness.The notes also document material concerning landfill hydrogen sulphide, machine-learning nowcasting, community-impact validation, and the causal hierarchy in main Fig. 2.Source: SUPPLEMENTARY INFORMATION · p. 47

Supplementary Methods

  • The six Supplementary Methods specify environmental characterisation, MSTE estimation, ALE analysis, the S4D state-space model, optimiser scheduling, and walk-forward validation.They include the KSG–Theiler estimator and pseudocode, ALE derivations, continuous-time SSM and ZOH details, loss and learning-rate procedures, and no-leakage validation with attribution and metric definitions.Source: SUPPLEMENTARY INFORMATION · pp. 47–48

Extended Data

The extended data establish that the production S4 configuration is defined by physics-anchored timescale initialization and that it outperforms the engineered benchmark on High-class detection, discrimination, and false-alarm metrics. They also define the meteorology-only multi-site alert-tier evaluation, including uncertainty procedures, baselines, and held-out external validation.

Initialization ablation

  • The production configuration uses physics-anchored timescale priors within a dual-pathway diagonal S4 architecture, with all other ablation factors held constant.The six-condition initialization ablation varied only SSM kernel initialization and per-lane ∆ bounds; the MSTE-aligned condition was the production configuration.Source: Table ED1 · p. 50, Extended Data · p. 50

Walk-forward performance

  • The S4 model led the engineered XGBoost benchmark on every High-class detection metric, discrimination, and false alarms, adding 38 true positives and reducing false positives by 14.These margins were modest and not significant across 13 paired folds (F1-High p = 0.110), but the paired decision over 8,040 predictions was significant (McNemar, 344 against 292, p = 0.043).Source: Table ED2 · p. 51
  • The S4 model marginally improved Brier-High, whereas XGBoost achieved better ranked probability score and log-loss after evaluation-block checkpoint selection was removed.Whole-distribution metrics were reported for completeness rather than as an operational target.Source: Extended Data · p. 51

Multi-site alert-tier classifier

  • The meteorology-only multi-site Bayesian alert-tier classifier was evaluated on 8,536 synchronous 15-minute timesteps with block-bootstrap confidence intervals, a vote-count baseline, and majority-class and κ baselines.The predicted tier used no raw target-species concentration at inference, while external validation against community odour complaints was fully held out; leave-one-week-out tuning optimism was ∆κw = 0.006.Source: Table ED3 · p. 52

S1 Regulatory and public-health context

Landfill fugitive emissions remain a persistent community risk because gas controls can fail, while H2S concentrations below acute-toxicity thresholds can still exceed the WHO odour-annoyance guideline and impair wellbeing. Current regulatory responses are largely post-exposure and rely on assessments or models that may not capture nonlinear, time-varying dispersion at real sites.

Waste, landfills and fugitive gas emissions

  • Landfills release methane, carbon dioxide and trace reduced sulphur gases, while imperfect containment and extraction can allow fugitive emissions to migrate to nearby communities.Global municipal waste generation is projected to rise from 2.01 billion tonnes per year to 3.40 billion tonnes by 2050. Poor-performing waste-sector sites are disproportionately implicated in pollution incidents and fugitive emissions.Source: Waste, landfills and fugitive gas… · p. 53

Hydrogen sulphide: toxicology and odour

  • The WHO 30-minute H2S odour-annoyance guideline is 7 µg m−3, far below acute-exposure thresholds, while prolonged or high concentrations can cause odour fatigue, irritation and severe toxicity.H2S odour thresholds are approximately 0.75–11 µg m−3, and high concentrations around 140 mg m−3 or above can cause collapse, respiratory paralysis, coma and death within minutes.Source: Hydrogen sulphide: toxicology and odour · p. 53

Odorous nuisance and the FIDOL framework

  • Environmental odour impacts vary across people and populations, and persistent exposure is associated with annoyance, sleep disruption, sensory irritation and other community health complaints.Surveys report that 13–20% of Europeans are bothered by environmental odours.Source: Odorous nuisance and the FIDOL framework · p. 53

Multi-stakeholder regulatory response

  • Regulatory response combines local-authority assessment, operator compliance oversight and public-health interpretation against WHO guideline values and AEGLs, escalating to multi-agency coordination when impacts become severe.The UK FIDOL framework assesses Frequency, Intensity, Duration, Offensiveness and Location, while statutory nuisance decisions incorporate sensory assessment, complaints and context.Source: Odorous nuisance and the FIDOL framework · p. 53, Multi-stakeholder regulatory response · p. 54
  • Risk assessment uses a source–pathway–receptor model, but communication and decisions generally follow exposure, while dispersion models depend on assumptions that may not match nonlinear, time-varying site conditions.The pathway is atmospheric dispersion shaped by meteorology and topography, and the receptor is the surrounding residential population.Source: Multi-stakeholder regulatory response · p. 54

Case study

  • At the case-study landfill, H2S often exceeded the WHO 7 µg m−3 odour guideline despite generally remaining below the ATSDR intermediate minimal-risk level, prompting sustained source-reduction efforts and additional wellbeing support.Community complaints rose from early 2021, multi-agency response structures were convened, and the regulator issued site closure at the end of 2024. The main-text analyses use anonymized, post-calibration-adjustment monitoring data from 2024.Source: Case study · p. 54

S2 Extended environmental characterisation

Extended analysis of 34,609 valid 15-minute MMF9 observations characterized hydrogen sulphide conditions and localized its likely source using wind-directional evidence. The westerly sector showed the strongest association, and all three stations triangulated a common emitting region.

S2 Extended environmental characterisation

  • The analysis used 34,609 valid 15-minute H2S observations from MMF9 in 2024, out of a complete grid of 35,136.All statistics used the principal receptor record unless otherwise stated.Source: S2 Extended environmental… · p. 54

Source attribution by Conditional Probability Function (Fig. 1a)

  • CPF peaked at bearing 265° in the westerly sector, with CPF ≈0.37 using a 5 µg m−3 exceedance threshold.The threshold was selected between the odour-detection threshold and the WHO 30-minute guideline value.Source: Source attribution by Conditional… · p. 54
  • 11.2 µg m−3 in W and 10.6 µg m−3 in NW contrasted with 1.1 µg m−3 in E, yielding a 4.09× peak/opposing-sector ratio.Wind direction and H2S concentration had circular–linear correlation r = 0.149 (p < 10−3, n = 34,609).Source: Source attribution by Conditional… · p. 55
  • Aligned wind direction elevated the odds of a concentration spike above the 95th percentile to 1.43 relative to background; associated correlation was r = 0.149 (p < 10−3).The spike threshold was 15.3 µg m−3.Source: Source attribution by Conditional… · p. 55
  • CPF cones from MMF9, MMF1, and MMF2 converged on a common source area, providing spatial triangulation of the emitting region.Source: Source attribution by Conditional… · p. 55

Chemical fingerprint: H2S–CH4 co-emission (Fig. 1b)

H2S shows strong, super-linear co-emission with CH4, while negative controls and multi-site analysis support gas-phase attribution. Diurnal, sunrise-aligned, and meteorological analyses identify stable, low-wind conditions and inversion dynamics as key concentration drivers.

Chemical fingerprint: H2S–CH4 co-emission (Fig. 1b)

  • H2S–CH4 co-emission was strong, with Pearson r = 0.830, Spearman ρ = 0.683, power-law exponent b = 1.95, and 1,386 spike coincidences versus 87.7 expected.The super-linear relationship is consistent with enhanced sulphate reduction at source, but the exponent also reflects dilution, oxidation, and gas-extraction effects at the receptor.Source: Chemical fingerprint: H2S–CH4… · p. 55

Negative controls

  • PM10 and PM2.5 showed no positive association with H2S, with r = −0.028 and r = −0.009, respectively, arguing against particulate resuspension.NOx correlation was moderate (r = 0.377) but its 08:00 LST peak lagged the 02:00 LST H2S peak by six hours, indicating nocturnal trapping rather than a shared source.Source: Negative controls · p. 55

Multi-site meta-analysis

  • Across four sites, pooled H2S–CH4 correlation was rpooled = 0.80 (95% CI: 0.74–0.84), satisfying the strong-attribution criterion despite high heterogeneity (I2 = 99.8%).Site differences reflected source distance and local wind channelling.Source: Multi-site meta-analysis · p. 55

Temperature–H2S diurnal hysteresis (Fig. 1c)

  • Temperature–H2S trajectories showed strong hysteresis (A∗ = 0.369), whereas wind-speed–H2S hysteresis was negligible (A∗ = 0.012), indicating effectively memoryless dilution.Cooling and warming slopes were βcool = −2.83 and βwarm = −2.45, with Hindex = 0.072.Source: Temperature–H2S diurnal hysteresis… · pp. 55–56

Diurnal concentration profile (Fig. 1d)

  • H2S peaked at 02:00 LST (mean 9.69 µg m−3) and troughed at 14:00–15:00 LST (mean 1.31 µg m−3), yielding a 7.4× mean peak/trough ratio.The February peak was 14.97 µg m−3 versus 0.99 µg m−3 in August, a 15.1× seasonal ratio.Source: Diurnal concentration profile (Fig. 1d) · p. 56

Sunrise-aligned inversion break-up (Fig. 1e)

  • Sunrise-aligned concentrations fell 7.3× from the pre-sunrise baseline, declining from 10.42 µg m−3 at −2 h to 1.30 µg m−3 by +4 h.The pattern was reproduced across all 365 calendar days and was statistically significant (Mann–Whitney p < 10−15).Source: Sunrise-aligned inversion break-up… · p. 56

Bivariate mechanism scatter (Fig. 1f)

  • Low wind strongly elevated H2S: mean concentration was 11.8 µg m−3 below 1 m s−1 versus 1.8 µg m−3 above 5 m s−1, a 6.5× difference.Extreme spikes clustered in low-wind, low-temperature, negatively cooling stable boundary layers, despite individual mechanism R2 values of only 0.015–0.030.Source: Bivariate mechanism scatter (Fig. 1f) · p. 56

S3 Per-season interpretation of the XGBoost ALE feature hierarchy

Corrected causal classifiers reveal season-dependent ALE hierarchies: diurnal timing dominates winter, spring, and autumn, whereas wind speed leads in summer. Agreement with transfer entropy is partial, reflecting shared wind signals but differing treatment of calendar structure and atmospheric pressure.

S3 Per-season interpretation of the XGBoost ALE feature hierarchy

  • Correcting the centred temperature-tendency window to be strictly causal removes that feature from the leading group in all four seasons and changes the interpretation.The corrected importances are class-mean values; the earlier feature carried approximately three hours of lookahead.Source: S3 Per-season interpretation of the… · p. 57

Winter (January–March)

  • Winter has the flattest, weakest hierarchy: no feature exceeds ¯I = 0.04, with hour cos leading at ¯I = 0.037 and temperature tendency below ¯I < 0.001.The near-default nocturnal inversion in short winter days leaves no single meteorological discriminator sharply separating exceedance from background.Source: Winter (January–March) · p. 57

Spring (April–June)

  • Spring has the most even hierarchy, with hour cos at ¯I = 0.146 and stagnation 2h at ¯I = 0.130, while summer uniquely places wind speed first at ¯I = 0.058.Spring stagnation is informative because it departs from generally well-ventilated conditions; summer reflects convective mixing and mechanical dilution.Source: Spring (April–June) · p. 57, Summer (July–September) · p. 57

Autumn (October–December)

  • Autumn has the strongest seasonal attribution: diurnal timing reaches ¯I = 0.333, roughly an order of magnitude above stagnation 2h at 0.037.Shortening daylight and longer nocturnal stable-boundary-layer periods make time of day a proxy for stability state.Source: Autumn (October–December) · p. 57

Cross-seasonal consistency with the causal hierarchy

  • Across seasons, diurnal timing leads in winter, spring, and autumn, while wind speed leads in summer; wind speed and direction remain prominent throughout.This supports wind transport as a recurring exceedance signal, with mechanical dilution displacing stability timing under summer convection.Source: Cross-seasonal consistency with the… · pp. 57–58
  • The apparent ranking differences are structural: ALE credits calendar terms with diurnal patterns, whereas transfer entropy conditions on target history; raw pressure receives zero ALE importance because stagnation encodes its synoptic content.The shared diurnal structure accounts for only 2.7% of effective transfer entropy, and the methods differ as their definitions predict.Source: Cross-seasonal consistency with the… · p. 58
  • ALE and transfer entropy agree on their seven shared features’ leading pair: wind speed ranks first (¯I = 0.029) and WD sin second (0.017).The remaining five shared features, including all three tendency variables, fall below ¯I = 0.002.Source: Cross-seasonal consistency with the… · p. 58

S4 Extended comparison with prior literature

The section situates the study’s causal hierarchy, physics-anchored architecture, and community-impact validation against prior landfill, environmental forecasting, and public-health work. It also identifies measurement, transferability, and operational constraints that must be addressed before deployment.

Causal hierarchy versus mobile-laboratory and cover-type surveys

  • The MSTE hierarchy aligns with established landfill mechanisms: advection selects the exposed receptor, wind controls dilution, pressure changes modulate source flux, and boundary-layer mixing governs receptor exposure.The study’s multi-season record provides temporal coverage for causal testing beyond surveys reporting days-to-weeks of co-located measurements, including Catena et al. and California Air Resources Board. Its dP/dt threshold at τ ≥2 h corresponds to experiments showing 20-fold breakthroughs in under 24 h [19], while hysteresis and H2S–CH4 scaling agree with independent soil–gas and mobile-laboratory findings.Source: Causal hierarchy versus… · pp. 58–59

Physics-anchored architectural prior versus data-agnostic SSM initialisation

  • The six-condition ablation finds the best slow-anchor timescale among 6, 48, and 147 h within the pressure-causality band, outperforming every tested initialization with q ≤0.048.The sweep did not test anchors between 6 and 48 h, so the optimum is identified only within the tested set. The model also reproduces dP/dt and dT/dt marginal responses without derivative inputs, while lane-resolved association remains weak (ρs = +0.14).Source: Physics-anchored architectural prior… · p. 59

Calibration to community impact versus hard threshold detection

  • Across a full quarter, a meteorology-only causal nowcaster’s internal probability tracked an independent community-wellbeing endpoint at 15-minute resolution (r = 0.585 at lag 0, n = 88 days), making outputs interpretable through FIDOL.The operational target is the much lower 30-minute WHO odour-annoyance guideline, not the regulatory acute-exposure threshold, because community impact is already substantial there.Source: Calibration to community impact versus… · pp. 59–60

Operational pathway and limitations

  • Operational protection requires auditable calibrated measurements, site-specific re-estimation of the causal hierarchy, and deployment of numerical-weather inputs, while clinical surveillance remains a longer-term validation opportunity.The study uses only a post-calibration-adjusted record, and landfill variability documented by Catena et al. and California Air Resources Board argues against unverified transfer. The forecasting pipeline is not yet built, although demonstrated 20–40% peak-pollutant reductions elsewhere define a realistic upper bound if dynamic extraction is co-deployed.Source: Operational pathway and limitations · p. 60

S5 MSTE estimator ablation study

The ablation shows that core causal drivers are robust to estimator choices, while conditioning and reduced history depth are necessary for physically interpretable transfer-entropy estimates. Split-half resampling largely preserves the recovered hierarchy, with wind speed at coarse scales the least robust element.

S5 MSTE estimator ablation study

  • The six-configuration ablation used identical data and preprocessing, but its B = 10 screen estimates stability rather than independent significance; production significance instead comes from B = 2,000 surrogates.At coarse scales, configurations 3–5 coincide because the adaptive history depth is already one, reducing genuinely independent estimator checks.Source: S5 MSTE estimator ablation study · pp. 60–61

Three principal findings

  • Wind direction, wind speed, and pressure remain significant across configurations, while conditional estimation suppresses bivariate false positives and reduced history depth removes spurious temperature significance.Configuration 6 gives dP/dt ETE values of 0.6–19.5 × 10^-3 nats across all scales, whereas conditional configurations detect it only at ≥2 h.Source: Three principal findings · p. 61

Justification of the production configuration

Dependence between tests

  • Benjamini–Yekutieli sensitivity analysis retains 20 of 29 significant cells, including all wind-direction and pressure cells, while excluding two interpretable cells: wind speed at 12 h and temperature at 15 min.The correction accounts for dependence among nested scales and deterministic tendency variables.Source: Dependence between tests · p. 61

Split-half stability of the recovered hierarchy

  • The driver hierarchy is stable across half-year samples: WDsin > Pressure > WS in both halves and the full year, with significance retained in 20/21 H1 and 18/21 H2 cells.Signs agree in 19 of 21 cells and half-to-half Spearman correlation is 0.623; the two sign disagreements are wind-speed cells at 6 h and 12 h, making coarse-scale wind speed least robust.Source: Split-half stability of the recovered… · p. 62
  • Because the split halves differ seasonally and cannot reveal uniform estimator bias, validation supports stability of the hierarchy rather than absolute transfer-entropy magnitudes or agreement with another estimator.The full-year estimate exceeds both half-year estimates for pressure and wind speed, consistent with sample-size-dependent bias.Source: Split-half stability of the recovered… · p. 62

S6 Joint site analysis

This section evaluates CAIRN’s joint site-level fusion of four meteorology-trained nowcasters into a continuous, four-tier alert, comparing it with sensor-based ground truth and independent community odour complaints. It also examines the fusion approach and the uncertainty associated with different alert tiers and weekly estimates.

S6 Joint site analysis

Ordinal alert tier definitions

Hysteresis debouncing

  • Hysteresis uses 3 consecutive 15-minute ticks to activate and 2 to clear, corresponding to a 45-minute onset and 30-minute clearance.The asymmetric latch suppresses isolated spikes while preventing resolution within a single WHO 30-minute averaging interval.Source: Hysteresis debouncing · pp. 63–64, Table S1 · p. 65

Posterior cut-points θ1, θ2, θ3

  • The deployed posterior cut-points are θ1=0.15, θ2=0.50, and θ3=0.92, with Tier 3 just below the analytical posterior ceiling of 0.949 for all four active channels.Leave-one-week-out refitting selected θ1=0.20 in all 13 folds, changing κw by 0.013; the held-out four-week subset achieved κw=0.528 and strict accuracy=0.716.Source: Posterior cut-points θ1, θ2, θ3 · p. 66

Likelihood ratios

  • Likelihood ratios were conservatively calibrated below constituent precision–prevalence ratios to absorb positive dependence from shared chemistry and meteorology, with ±25% perturbations changing headline κw by at most 0.009.H2S-quiet states provide mild negative evidence, CH4-quiet states are neutral, and missing channels contribute no evidence.Source: Likelihood ratios · pp. 67–68, Table S3 · p. 68, Inter-channel dependence · p. 69

Headline tier-match performance

  • The meteorology-only alert tier achieved substantial quadratic-weighted agreement with the deterministic raw-sensor ground truth across 8,536 shared-grid timesteps in Jan–Mar 2025.Agreement was evaluated with block-bootstrap uncertainty using 1,000 resamples and 24-hour blocks; the matched-block bootstrap standard error was 0.075.Source: Headline tier-match performance · pp. 70–71

Comparison to a vote-count baseline.

Per-week tier-match performance.

  • The pooled classifier achieves κw = 0.709 (95% CI 0.557, 0.852) and strict accuracy 0.794, but weekly κw is unstable when tier support falls below approximately 10.Week 7 has no ground-truth deviations, making κw undefined, while its accuracy of 0.970 serves as a specificity check rather than a general agreement estimate.Source: Table S6 · p. 71, Per-week tier-match performance · p. 72, Table S7 · p. 72

Effective sample size at the extremes.

Daily-mean alert tier versus daily complaints.

Lagged cross-correlation.

  • The unique lag-0 maximum (r = 0.729), versus r = +0.575 at −1 day and +0.552 at +1 day, confirms alignment with contemporaneous community exposure.Correlations fall to r ≤0.40 at absolute lags of at least two days.Source: Lagged cross-correlation · pp. 72–73, Table S8 · p. 73

Operational implication and limitations.

  • Tier 0 achieves F1 = 0.91, while Tier 3 reaches F1 = 0.57 with recall 0.49; intermediate tiers show larger off-by-one errors, with F1 approximately 0.35.Tier 0 represents 80% of the validation window, whereas roughly half of Tier 3 episodes are correctly flagged from meteorology alone; Tier 1 is over-triggered and Tier 2 under-triggered.Source: Table S6 · p. 71, Operational implication and limitations · p. 73

Supplementary Methods

This supplementary section provides the mathematical, procedural, and training specifications for environmental characterisation, causal analysis, CAIRN’s multiscale S4D architecture, evaluation, and interpretation. It also documents data-quality limitations, reproducible significance-testing choices, and the method-dependent nature of lane-ablation contributions.

Environmental characterisation

Temporal coarse-graining

  • At τ ≥24 h, every coarse-scale block contains filled or missing slots, so those estimates are descriptive and additionally sample-limited; at 6 h, 31.0% of blocks are affected.The stricter MSTE rule retains n = 89 at 96 h, which is reported as not estimable.Source: Temporal coarse-graining · p. 76

Multiscale transfer entropy

Surrogate testing

  • Significance testing uses 2,000 circular-shift surrogates that preserve source autocorrelation, periodicity, and marginal distribution while disrupting temporal alignment, followed by Benjamini–Hochberg correction at α = 0.05.The surrogate mean is exactly reproducible from fixed seeds, whereas the estimator ablation uses only B = 10 and is reported as a coarse screen.Source: Surrogate testing · pp. 77–78

Accumulated Local Effects

  • ALE estimates centred local feature effects within observed quantile intervals, separately for Low, Medium, and High class probabilities, with held-out validation curves and class-averaged importance.This approach avoids extrapolation into unlikely feature regions and is intended to remain unbiased when meteorological predictors are correlated.Source: Accumulated Local Effects · p. 79, Definition · p. 79, Multiclass aggregation · p. 79

S4D state space model

Causality guarantees

  • Strict causality is enforced through non-negative SSM kernels, explicit causal FFT truncation, and final-timestep pooling rather than bidirectional or global pooling.The kernel length must equal the input length, and the representation passed to the heads is hL−1, preserving a single prediction-time receptive field.Source: Causality guarantees · p. 81

Production hyperparameters

  • The production model uses H = 128, N = 256, three layers, a 384-step 96-h context, a 0.5 fast/slow split, dropout 0.29, and DropPath pmax = 0.15.The S4D block uses Pre-Norm, sigmoid-gated linear units, zero-initialised skips, and stochastic depth to stabilise deep residual training and preserve slow-lane information.Source: S4D block · p. 81, Production hyperparameters · p. 82

Joint loss

  • The joint objective assigns λcls = 1.0 and λreg = 0.0, so reported results train only focal classification with γ = 2.62 and class weights (1.00, 11.26, 14.07).Manual weighting emphasises High-class performance and focuses updates on borderline Medium–High examples, while inverse-prior sampling approximately balances minibatch class marginals despite a ∼13:2:1 imbalance.Source: Joint loss · p. 82

Optimiser schedule

  • Training uses differential AdamW rates, six frozen warmup epochs for A parameters, validation High-class F1 scheduling, seven-epoch early stopping, and a 60-epoch maximum.SSM parameters use ηs4 = 10^-4 and ηA = 10^-4, gradients are clipped at norm 1.0, and the scheduler halves learning rates after two plateau epochs to a 10^-5 floor.Source: Differential learning-rate groups · p. 82, Warmup and freeze schedule · p. 82

Walk-forward validation

  • Walk-forward evaluation uses 13 independent weekly retrains with expanding training windows, a 383-step context reserve, training-only scaling, fresh model initialisation, and sample-size-weighted metric aggregation.The validation horizon spans 1 October–31 December 2024; labels in the context reserve are never back-propagated, and the aggregate metrics appear in Extended Data Table ED2 and Supplementary Table 5.Source: Validation horizon and training cutoff · p. 83, Per-week pipeline · p. 83

No-leakage guarantees

  • The evaluation eliminates label, feature, model, hyperparameter, and retrain leakage while reporting hard, probabilistic, and WHO-aligned conditional-rolling metrics.Rolling metrics use a 4-h window at 15-min cadence, and false-alarm rate is defined as FAR = FP/(FP + TN) for High versus non-High.Source: No-leakage guarantees · pp. 83–84, Metric definitions · p. 84

Lane ablation

  • +0.121 interaction contribution exceeded the fast (+0.083) and slow (+0.074) lane contributions, while their paired difference was −0.002 and statistically indistinguishable.Under kernel-path masking, fast versus slow ordering reversed across aggregation rules; block-path masking instead gave the fast lane the larger contribution, so neither formulation uniquely establishes a lane-specific mechanism.Source: Lane ablation · pp. 84–85

Feature sensitivity over time

  • Feature sensitivity averages causal, lane-specific feature–lag contributions across 13 folds over the 96-h input window using kernel-derived analytical weights.Column normalisation produces fractional feature contributions at each lag for visualisation as stacked-area charts, while suppressing single-checkpoint noise.Source: Feature sensitivity over time · p. 85

Supplementary Tables

The supplementary tables document environmental exposure statistics, seasonal classification performance, transfer-entropy estimator checks, and cross-species transfer. They also show that CAIRN’s memory architecture improves High-class detection over memoryless and engineered-feature alternatives under a matched walk-forward design.

Seasonal classification

  • The seasonal XGBoost evaluation reports per-class precision, recall, and F1 plus quarterly accuracy, with High-class prevalence ranging from 5.2% in Summer to 12.8% in Winter.Season-specific hyperparameters were selected using temporally isolated one-week holdouts, and validation and evaluation F1 agreed within |∆F1| ≤0.009.Source: Table S11 · p. 87, Table S10 · p. 87, Table S12 · p. 88

Cross-species transfer and data handling

  • The same S4 architecture transfers to co-emitted CH4 under a common protocol, while six Autumn Low-class samples are omitted after a seven-hour meteorological outage because causal derivatives require longer history.The omitted samples do not change Medium or High counts.Source: Supplementary Tables · p. 87, Table S14 · p. 89

Transfer-entropy analysis

  • Transfer-entropy supplementary tables compare effective transfer entropy across 42 driver–scale combinations and six estimator configurations, identifying configuration 4 as the production setup for main Fig. 2.At B = 10, surrogate screening is coarse and not false-discovery-corrected; significance for the main result comes from the production run at B = 2,000.Source: Table S14 · p. 89, Table S15 · p. 89, Table S16 · p. 90

Memory ablation

  • The three-arm decomposition used the same walk-forward protocol and 8,040 evaluation timesteps, isolating memoryless raw inputs, engineered memory, and CAIRN state-space memory.CAIRN’s ordering was monotone on every High-class metric and false alarms, but it ranked last on overall accuracy and multiclass log-loss because focal loss and High-class weighting favor sensitivity.Source: Table S18 · p. 91
  • CAIRN improved pooled High-class F1 by +0.073 over memoryless XGB-16, while engineered features improved it by +0.040; both increments passed paired Wilcoxon tests, but neither passed the two-sided sign test.The architecture increment had p = 0.022 and the engineering increment p = 0.027; sign-test p = 0.092 for both.Source: Supplementary Tables · p. 91
  • The ordering XGB-16 < XGB-24 < CAIRN survived every jackknife, while the CAIRN–XGB-24 endpoint difference was +0.032 and not statistically conclusive.The endpoint difference had p = 0.110 and bootstrap 95% CI [−0.017, +0.081].Source: Supplementary Tables · p. 91

Supplementary Figures

Supplementary Fig. S1 shows strong concurrent coupling between co-located H2S and CH4 measurements, supporting the cross-species transfer experiment.

Cross-species CH4 nowcaster

  • Strong concurrent coupling between H2S and CH4 at the principal receptor underpins the cross-species CH4 nowcaster transfer experiment.The autumn 2024 walk-forward validation window used co-located 15-minute measurements and a linearly corrected H2S–CH4 class-boundary scale.Source: Figure S1 · p. 92

Related papers

Loading 2608.14254v1…