Meteorology-driven Causal Nowcasting of Fugitive Landfill Emissions from Measured Coupling Timescales

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

cs.CYAug 14, 2026

Meteorology-driven Causal Nowcasting of Fugitive Landfill Emissions from Measured Coupling Timescales

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

Organizations: Biomedical Engineering Research Group, School of Engineering, University of Leicester, Leicester, United Kingdom. · Environmental Hazards and Emergency Department, UKHSA, Nottingham, United Kingdom.

Abstract

Which meteorological processes control exposure to fugitive gases downwind of a source, and on what timescales, have largely been inferred from dispersion theory and partial field evidence. Here we show that the meteorological drivers of elevated hydrogen sulphide (H $_2$ S) exposure at a long-monitored European landfill, and the timescales over which each acts, can be identified directly from monitoring data. Wind direction, wind speed and atmospheric pressure form the causal core, with the share of directed information carried by pressure increasing with aggregation scale. The recovered timescales are consistent with those expected from the underlying atmospheric processes. We use these driver timescales to initialise CAIRN (Causal-Anchored Inference for Receptor Nowcasting), a machine-learning nowcaster with fast and slow memory components. Trained on past exceedances of WHO guideline levels, CAIRN nowcasts them from surface weather measurements and the calendar alone, without hand-engineered features. Combining four such nowcasters produces a site-level, tiered alert that agrees substantially with that generated by a direct sensor network and tracks an independent record of community odour reports. Meteorological variables can therefore serve as an inference-time proxy for exposure relative to WHO guideline levels, and they link atmospheric dynamics to community impact as an episode unfolds.

Figures & tables

Figure 1: Caption continued on next page.

Figure 2: Multiscale information flow from meteorology to hydrogen sulphide. a , Effective transfer entropy (ETE; nats) from each of seven candidate meteorological drivers to H 2 S, evaluated at ten temporal scales ( $\tau=15$ min to $96$ h), of which the nine estimable scales ( $\tau=15$ min to $48$ h) are displayed; row colours identify each driver (shared with panel b). Cell values give ETE in nats. Colour intensity encodes ETE relative to that cell’s own surrogate standard deviation, because raw ETE is not comparable across scales (Methods); asterisks denote significance after Benjamini–Hochberg false-discovery-rate correction across a single family of all 70 tests ( ${}^{**}\,p_{\mathrm{adj}}\leq 0.025$ ; ${}^{*}\,0.025<p_{\mathrm{adj}}<0.05$ ). Filled symbols mark cells that additionally survive Benjamini–Yekutieli correction, which is valid under arbitrary dependence; open symbols mark cells significant under Benjamini–Hochberg alone. Of the 29 cells reaching significance, 20 are filled and 9 open; 18 of the 19 cells belonging to the three directly measured core drivers are filled, the exception being wind speed at 12 h. Seven of the nine open cells are meteorological tendency variables and the remaining two are wind speed at 12 h and temperature at 15 min. The seven cells of the 96 h row are retained in the correction family although not estimable and not displayed, so the figure shows 63 of the 70 tested cells while the multiplicity penalty is applied across all 70. The three tendency-variable rows are shown in grey: they are deterministic transforms of drivers already present in the family, retained so that the Benjamini–Hochberg correction is applied across all 70 tests, but not interpreted in the main text (Supplementary Note 5). b , Stacked-bar decomposition of total positive ETE by driver at each temporal scale. Segment fills and stacking order match panel a; numerals give the cumulative total per scale; asterisks follow the same FDR threshold as panel a and are shown only for segments tall enough to carry a marker. Scales at which no cell reaches significance are labelled n.s. Estimator and confounder selection: Methods, “Causal analysis” ( $B=2{,}000$ circular-shift surrogates). Sensitivity to estimator hyperparameters in Supplementary Note 5.

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Metric	XGBoost	CAIRN	$\Delta$
High-class detection metrics (argmax of the three-class posterior)
F 1 -High	0.501	0.533	$+0.032$ ( $+6.3\%$ )
Recall-High	0.575	0.618	$+0.044$ ( $+7.6\%$ )
Precision-High	0.445	0.468	$+0.024$ ( $+5.3\%$ )
False-alarm rate	0.087	0.085	$-0.002$
Discrimination

Table 2: Period-wide walk-forward performance of CAIRN versus the engineered XGBoost benchmark under a matched selection protocol. Pooled across the 13 weekly walk-forward retrains over Oct–Dec 2024 (

n=8{,}040

evaluation timesteps) on the case-study site; both models select their stopping point on the same 7-day inner temporal probe, and the decision rule is the argmax of the three-class posterior. CAIRN leads on every High-class detection metric, on discrimination and on false alarms, contributing 38 additional true positives while producing 14 fewer false positives. The individual margins are modest and none reaches significance on a paired per-fold test over the 13 folds (F 1 -High

p=0.110

); the paired High-class decision over all 8,040 predictions does (McNemar, 344 against 292,

p=0.043

). The probabilistic terms separate from the detection terms: Brier-High marginally favours CAIRN, while the ranked probability score and log-loss favour the benchmark, reflecting that inner-probe checkpoint selection yields a better-ranked but less well-calibrated posterior (Results, “Walk-forward performance”). Whole-distribution metrics are reported for completeness and are an operational target of neither model. Weekly per-fold breakdown in Supplementary Table S13 .

Symbol	Value	Interpretation
$C^{\mathrm{H_{2}S}}_{\mathrm{thr}}$	$7.0\,\mu\mathrm{g\,m^{-3}}$	WHO 30-min odour-annoyance guideline value (Note 1); ground-truth activation threshold for each H 2 S channel and the training boundary that defined the High class for the H 2 S CAIRN nowcasters
$C^{\mathrm{CH_{4}}}_{\mathrm{thr}}$	$2.756\,\mathrm{ppm}$	Linear High-class boundary from $\mathrm{H_{2}S}=5.55\,\mathrm{CH_{4}}-8.29$ (Supplementary Table S14 ); ground-truth activation threshold for each CH 4 channel and the training boundary that defined the High class for the CH 4 CAIRN nowcasters
$p^{\star}$	$0.50$	Grid-search parameter (range $0.30$ – $0.50$ ); binarises model probability $p_{c,t}$ before the hysteresis latch
$N_{\mathrm{on}}$	$3$ ticks (45 min)	Minimum sustained-event window: one full 30-min WHO averaging interval plus a 15-min safety margin against single-tick voltage transients
$N_{\mathrm{off}}$	$2$ ticks (30 min)	Matches the WHO 30-min averaging window so the latch will not declare an episode resolved within a single regulatory averaging interval
$\pi$	$0.10$	Grid-search parameter (range $0.03$ – $0.10$ ); at the selected value the classifier reverts to the observed network-wide High-class rate when all channels are missing, i.e. is neutrally calibrated at zero information

Table S1: Ordinal alert tier classifier parameters and the interpretation attached to each. The concentration thresholds follow from the regulatory and physiological levels reviewed in Supplementary Note 1. The hysteresis counts, the prior

\pi

, the per-channel activation threshold

p^{\star}

and the likelihood ratios were grid-search parameters, and the tier cut-points are operational choices that the documented search does not reproduce; the third column states how each value is interpreted, not how it was derived. Provenance for each is given in “Bayesian classifier parameter set” below, and the

\pm 25\%

likelihood-ratio sensitivity analysis is in Supplementary Table S4 . The latched-state hysteresis counts

(N_{\mathrm{on}},N_{\mathrm{off}})=(3,2)

correspond to (45 min onset, 30 min clearance) at the 15-minute grid. No raw-sensor concentration enters the predicted tier; the classifier is meteorology-only at inference time.

Configuration	$\kappa_{w}$	Odour-report $r$	Isolates
Selected parameters, whole window	0.669	$+0.711$	In-sample reference; mixed, nine weeks in sample and four held out
Stratified held-out weeks $\{1,3,8,10\}$	0.473	—	Fixed-configuration generalisation to a four-week subset
Leave-one-week-out refit	0.661	$\mathbf{+0.698}$	Fusion-parameter tuning optimism
Constrained-ordering leave-one-week-out	0.638	—	Sensitivity to the likelihood-ratio ordering

Table S2: Decomposition of the alert-tier agreement by what each configuration holds out. All rows use the identical four constituent nowcasters, ground-truth construction and Jan–Mar 2025 window; they differ only in which fusion parameters were fitted on the data being scored. The

0.473

subset figure and the

0.661

leave-one-week-out figure differ because the former scores a single four-week subset under one fixed configuration, while the latter concatenates held-out predictions across all thirteen weeks; the subset figure’s deviation from the whole-window value reflects week-composition variance, not additional tuning bias — which the leave-one-week-out comparison isolates at

0.008

. All rows use the retrained constituent nowcasters (“Checkpoint selection for the fused channels”, below); with checkpoints selected on the evaluation week the four values are

0.709

0.528

0.703

and

0.692

Channel	Native precision	$\mathrm{LR}^{\mathrm{on}}_{c}$	$\mathrm{LR}^{\mathrm{off}}_{c}$	$\mathrm{LR}^{\mathrm{NaN}}_{c}$
H 2 S @ MMF9 (broad-coverage)	0.526	2.00	0.50	1.00
H 2 S @ MMF2 (tight-coverage confirmer)	0.636	3.00	0.50	1.00
CH 4 @ MMF9 (chemical corroboration)	0.632	7.00	1.00	1.00
CH 4 @ MMF2 (chemical corroboration)	0.673	4.00	1.00	1.00

Table S3: Channel-state likelihood ratios for the Bayesian fusion stage. Each ratio is the multiplicative update applied to the prior odds when the corresponding channel is in the indicated state (Eq. ( S4 )). Active-state values are calibrated multipliers, substantially smaller than the bare precision-prevalence ratio of each constituent nowcaster (column 2; the bare ratio is in the range

10

–

19

across the four channels at

\pi=0.10

) to account for inter-channel dependence (shared chemistry between H 2 S receptors, between CH 4 receptors, and between species at the same receptor). H 2 S-quiet states carry moderate negative evidence because the H 2 S channels are the most direct receptor measurements of the public-health-relevant species; CH 4 -quiet states carry

\mathrm{LR}=1

because the higher CH 4 background would make suppressive quiet evidence operationally unsafe. Missing data is always neutral. Robustness of these values is established by the

\pm 25\%

sensitivity analysis of Supplementary Table S4 . Native precision is that of the constituent nowcasters on which the likelihood ratios were selected; the same likelihood ratios are used for the retrained nowcasters reported in the main text.

Perturbed parameter	Factor	$\kappa_{w}$	$\Delta\kappa_{w}$
H 2 S MMF9 $\mathrm{LR}^{\mathrm{on}}$	$\times 0.75$	0.669	$+$ 0.000
H 2 S MMF9 $\mathrm{LR}^{\mathrm{on}}$	$\times 1.25$	0.669	$+$ 0.000
H 2 S MMF2 $\mathrm{LR}^{\mathrm{on}}$	$\times 0.75$	0.669	$+$ 0.000
H 2 S MMF2 $\mathrm{LR}^{\mathrm{on}}$	$\times 1.25$	0.666	$-0.003$
CH 4 MMF9 $\mathrm{LR}^{\mathrm{on}}$	$\times 0.75$	0.668	$+$ 0.000
CH 4 MMF9 $\mathrm{LR}^{\mathrm{on}}$	$\times 1.25$	0.669	$+$ 0.000

Table S4:

\pm 25\%

perturbation sensitivity of the window-wide tier-match

\kappa_{w}

to each active-state likelihood ratio. Each row scales one

\mathrm{LR}^{\mathrm{on}}_{c}

by the indicated factor with all other parameters held fixed (other LRs, hysteresis, prior, tier cut-points).

\Delta\kappa_{w}

is the deviation from the baseline

\kappa_{w}=0.669

. The maximum absolute deviation is 0.003 (one row), indicating that the headline performance is robust to the precise LR choice.

	Predicted $\tau_{t}$
Ground truth $\tau^{\mathrm{GT}}_{t}$	Tier 0	Tier 1	Tier 2	Tier 3	Support
Tier 0	5,762 (84%)	791 (12%)	230 (3%)	43 (1%)	6,826
Tier 1	261 (37%)	274 (38%)	168 (24%)	10 (1%)	713
Tier 2	113 (19%)	197 (33%)	213 (36%)	70 (12%)	593
Tier 3	17 (4%)	39 (10%)	134 (33%)	214 (53%)	404

Table S5: Confusion matrix of predicted versus ground-truth ordinal alert tiers across the Jan–Mar 2025 validation window (

n=8{,}536

synchronous 15-min timesteps). Rows are the ground-truth tier

\tau^{\mathrm{GT}}_{t}

; columns are the meteorology-only predicted tier

\tau_{t}

. Diagonal cells are typeset in bold. Parenthesised values are row percentages.

Tier	Precision	Recall	F 1	Support	Population share
Tier 0	0.936 [0.916, 0.958]	0.844 [0.793, 0.888]	0.888 [0.855, 0.916]	6,826	79.9%
Tier 1	0.211 [0.136, 0.288]	0.384 [0.297, 0.459]	0.272 [0.191, 0.346]	713	8.4%
Tier 2	0.286 [0.189, 0.387]	0.359 [0.229, 0.511]	0.318 [0.219, 0.411]	593	6.9%
Tier 3	0.635 [0.363, 0.801]	0.530 [0.275, 0.751]	0.578 [0.320, 0.722]	404	4.7%
Macro avg	0.517	0.529	0.514	8,536	—
Accuracy	0.757		—	8,536	—

Table S6: Per-tier and macro classification metrics for the meteorology-only multi-channel Bayesian tier classifier. Block-bootstrap 95% CIs (

B=1{,}000

, block = 24 h) in brackets. Window-wide

\kappa_{w}=0.669

(CI 0.565, 0.755); strict element-wise accuracy 0.757.

Wk	$\kappa_{w}$	95% CI	Acc.	Tier 0	Tier 1	Tier 2	Tier 3	$n_{\mathrm{wk}}$
				Ground-truth tier support
1	0.461	[0.376, 0.530]	0.509	423	82	132	27	664
2	0.613	[0.565, 0.662]	0.423	314	19	120	219	672
3	0.370	[0.310, 0.432]	0.448	538	33	26	75	672
4	0.353	[0.255, 0.444]	0.771	609	21	42	0	672
5	0.359	[0.260, 0.441]	0.720	604	50	18	0	672

Table S7: Per-week tier-match performance with bootstrap 95% CIs. Each row reports the within-week quadratic-weighted Cohen’s kappa, strict element-wise accuracy, and the per-tier support counts in the ground-truth labels. Bold marks weekly blocks with point estimate

\kappa_{w}\geq 0.70

. Bootstrap CIs (

B=1{,}000

, within-week resampling) capture sampling variation within the week and do not account for cross-week autocorrelation. Week 7 has degenerate (

\kappa_{w}

undefined) tier variation.

Lag (days)	$-7$	$-6$	$-5$	$-4$	$-3$	$-2$	$-1$	$\mathbf{0}$	$+1$	$+2$	$+3$	$+4$	$+5$	$+6$	$+7$
Pearson $r$	0.34	0.24	0.21	0.15	0.18	0.39	0.54	0.71	0.59	0.34	0.24	0.22	0.31	0.34	0.42

Table S8: Lagged Pearson cross-correlation between daily-mean CAIRN predicted tier and daily community complaint count (

n=89

days,

\pm 7

-day window). Lag is in days; lag

>0

means the model leads odour reports. The unique global maximum at lag 0 indicates nowcast alignment at daily resolution.

Panel	Statistic	Value
Source attribution (Fig. 1a)
	Peak CPF bearing	$265^{\circ}\ \mathrm{(W)}$
	Peak CPF value	$\approx 0.37$
	Peak/opposing-sector ratio	$4.09\times$
	Sector-mean (W, NW, E)	$11.2$ , $10.6$ , $1.1\,\mu\mathrm{g\,m^{-3}}$
	Spike threshold (P95)	$15.3\,\mu\mathrm{g\,m^{-3}}$

Table S9: Quantitative summary of the environmental characterisation of receptor-level H 2 S exposure (main Fig. 1). All statistics are evaluated at the principal receptor (MMF9,

n=34{,}609

15-minute records with valid H 2 S across 2024) unless otherwise indicated.

Parameter	Winter	Spring	Summer	Autumn
max_depth	3	7	7	5
$\eta$ (learning rate)	0.092	0.118	0.132	0.040
n_estimators	150	100	150	300
subsample	0.883	0.978	0.832	0.981
colsample_bytree	0.798	0.790	0.789	0.740
$\alpha$ (L 1 )	0.078	1.131	0.326	0.930

Table S10: Optimal hyperparameters selected by Bayesian Tree-structured Parzen Estimator optimisation for each seasonal XGBoost classifier. Each season uses an independent one-week holdout for hyperparameter validation, temporally isolated from the evaluation quarter by a one-week gap.

		Low			Medium			High
Season	Acc.	P	R	F 1	P	R	F 1	P	R	F 1
Winter	0.764	0.887	0.851	0.869	0.536	0.573	0.554	0.523	0.583	0.551
Spring	0.817	0.962	0.848	0.902	0.567	0.739	0.642	0.402	0.644	0.495
Summer	0.836	0.980	0.864	0.918	0.355	0.631	0.455	0.474	0.749	0.581
Autumn	0.778	0.963	0.826	0.889	0.386	0.591	0.467	0.392	0.600	0.474
Annual (sample-weighted)	0.799	see per-class rows above

Table S11: XGBoost seasonal classification performance on the 2024 calendar-year evaluation periods. Precision (P), recall (R) and F 1 score are reported per class; accuracy summarises overall performance on the evaluation quarter. Sample counts per class are given in the lower block; the High-class fraction varies from

5.2\%

in Summer to

12.8\%

in Winter, reflecting seasonal emission and dispersion patterns.

Season	Search macro-F 1	Evaluation macro-F 1	$\Delta$ F 1
Winter	0.649	0.658	$+$ 0.009
Spring	0.676	0.679	$+$ 0.003
Summer	0.658	0.651	$-$ 0.006
Autumn	0.617	0.610	$-$ 0.007

Table S12: Comparison of XGBoost hyperparameter-search validation macro-F 1 (one-week holdout) and seasonal evaluation macro-F 1 (full quarter). The small differences (

|\Delta\mathrm{F}_{1}|\leq 0.009

) are consistent with little hyperparameter overfitting under the temporal isolation strategy.

Wk	S4	XGB	S4	XGB	S4	XGB	S4	XGB	S4	XGB	$n_{\mathrm{H}}$
	F 1 High $\uparrow$		Recall $\uparrow$		Precision $\uparrow$		FAR $\downarrow$		Brier H $\downarrow$
0	0.807	0.617	0.902	0.569	0.730	0.674	0.028	0.023	0.026	0.037	51
1	0.527	0.538	0.744	0.641	0.408	0.463	0.068	0.047	0.048	0.046	39
2	0.588	0.276	0.625	0.500	0.556	0.190	0.007	0.029	0.011	0.021	8
3	0.506	0.585	0.568	0.838	0.457	0.449	0.059	0.089	0.051	0.047	37
4	0.381	0.485	0.679	0.755	0.265	0.357	0.165	0.119	0.088	0.076	53

Table S13: Weekly walk-forward classification performance: S4 SSM versus XGBoost over the Oct–Dec 2024 validation window. Recall, precision and FAR are computed by taking the argmax of the three-class posterior; F 1 is the High-class harmonic mean. The argmax rule is not equivalent to thresholding

P(\mathrm{High})

0.5

: the latter would give 531/565/341 rather than the reported 539/612/333 true positives, false positives and false negatives. Bold entries are the weekly winner per metric.

n_{\mathrm{H}}

is the number of true High-class observations in the week. The weekly counts total 872 (mean 67.1). Period-wide aggregate counts are in main-text Table 2 . Aggregation convention: the

\bar{x}

row is the unweighted mean of the 13 weekly values. main-text Table 2 instead pools the confusion counts over all 8,040 timesteps before computing each metric, so the two tables report 0.528 (unweighted weekly mean) and 0.533 (pooled) for the same quantity. The pooled value is the larger of the two because the weeks with the smallest High-class support are also the weakest and an unweighted mean gives them disproportionate influence.

	S4 H 2 S					S4 CH 4
Wk	F 1	Prec	Rec	Brier	LL	F 1	Prec	Rec	Brier	LL
1	0.807	0.706	0.941	0.026	0.079	0.870	0.803	0.950	0.023	0.076
2	0.563	0.453	0.744	0.045	0.145	0.622	0.472	0.911	0.065	0.192
3	0.588	0.556	0.625	0.011	0.037	0.576	0.436	0.850	0.026	0.079
4	0.505	0.414	0.649	0.053	0.151	0.769	0.625	1.000	0.034	0.111
5	0.411	0.288	0.717	0.091	0.260	0.621	0.465	0.935	0.084	0.246

Table S14: Weekly walk-forward performance of the two S4 models on their respective High-class targets. CH 4 thresholds are obtained from the H 2 S thresholds by inverting the linear fit

\mathrm{H_{2}S}=5.55\,\mathrm{CH_{4}}-8.29

. Bold highlights the higher per-week value for the species pair on F 1 -High. Both columns use checkpoint selection on the evaluation week, not the inner-probe protocol of main-text Table 2 and Supplementary Table S13 . Evaluation-week selection is applied to both models so that the cross-species comparison uses a common protocol. The H 2 S values here therefore differ from Supplementary Table S13 – period-mean F 1 -High

0.577

against

0.528

– and the difference is attributable to the selection protocol rather than the model. The table shows that the same architecture transfers to a co-emitted species under a common protocol; it is not part of the benchmark comparison.

ID	Description	$h_{\max}$	Confounders	$k$	$\varepsilon$ -correction
1	Baseline	4	1	10 (fixed)	No
2	+ Boundary correction ( $\varepsilon$ -shrinkage)	4	1	10 (fixed)	Yes
3	+ Adaptive $k$	4	1	adaptive (Methods)	Yes
4	+ Reduced history ( $h\leq 2$ )	2	1	adaptive (Methods)	Yes
5	+ Minimal conditioning ( $h=1$ )	1	1	adaptive (Methods)	Yes
6	Bivariate (no conditioning)	1	0	adaptive (Methods)	Yes

Table S15: Ablation configurations for the KSG–Theiler conditional mutual information estimator used in the multiscale transfer entropy analysis. Each configuration is additive: subsequent rows inherit all preceding modifications and change a single additional parameter. Configuration 4 (bold) is the configuration used in main Fig. 2.

Core drivers (screened in nearly all configurations)
Driver	Scale	1 (B)	2 (BF)	3 (AK)	4 (RH)	5 (MC)	6 (BV)
WD sin	15 min	17.9*	20.0*	12.2*	18.1*	24.2*	42.6*
	1 h	23.5*	27.3*	18.6*	25.6*	33.1*	51.4*
	6 h	56.5*	61.6*	52.8*	52.8*	52.8*	64.0*
WS	15 min	10.1*	11.6*	5.3*	8.2*	10.5*	9.3*
	1 h	8.9*	10.1*	8.3*	12.8*	18.8*	22.4*

Table S16: Effective transfer entropy (ETE, nats

\times 10^{3}

) for each driver–scale combination under six estimator configurations. Columns labelled 1–6 refer to the configurations defined in Supplementary Table S15 . Asterisks mark cells in which zero of ten circular-shift surrogates exceeded the observed value; at

B=10

this is a coarse screen and not a false-discovery-corrected test (see the section text). Bold entries in column 4 indicate the configuration used in main Fig. 2. Dashes denote ETE

\leq 0

(no detectable coupling).

ID	Configuration	Mean ETE (nats)	Screened links (/42)	Notes
1	Baseline	$+0.0098$	27	Spurious TEMP significance (fine scales)
2	+ Boundary correction	$+0.0108$	27	Marginal improvement
3	+ Adaptive $k$	$+0.0083$	24	More conservative; fewer screened links
4	+ Reduced $h$	$+0.0088$	25	Selected bias–variance compromise
5	+ Minimal cond.	$+0.0099$	26	Loses $30$ min target memory
6	Bivariate	$+0.0143$	29	Inflated; confounders uncontrolled

Table S17: Aggregate ablation statistics across all 42 driver–scale combinations. “Screened links” counts the cells in which zero of ten circular-shift surrogates exceeded the observed transfer entropy. At

B=10

this is a coarse screen, not a false-discovery-corrected test; it is reported to compare stability across estimator settings, and the significance underpinning main Fig. 2 comes from the main analysis at

B=2{,}000

High-class detection
	XGB-16	XGB-24	CAIRN
Memory	none	hand-coded	learnt
Inputs	16 raw	24 engineered	16 raw
F 1 -High	0.4625	0.5013	0.5329
Precision-High	0.4000	0.4445	0.4683
Recall-High	0.5482	0.5745	0.6181

Table S18: Three-model decomposition isolating the contribution of memory. All three models share the walk-forward protocol, the 7-day adjacent inner probe, the argmax decision rule and the same 8,040 evaluation timesteps (872 High). They differ in one respect each. XGB-16 receives CAIRN’s sixteen raw inputs, none of which carries a lag, rolling window or derivative, and is therefore memoryless by construction; hyperparameters are tuned on the reduced set so the comparison is symmetric. XGB-24 adds the engineered feature set, in which Butterworth derivatives and stagnation indices supply memory by hand. CAIRN returns to the raw sixteen and supplies memory through the state-space kernels. Bold marks the best value in each row. The ordering is monotone on every High-class metric and on false alarms, but not on overall accuracy or multiclass log-loss, where CAIRN is last: its focal loss and High-class weighting trade specificity for sensitivity (Results).

Statistic	Value
Headline tier-match against the deterministic ground truth
Quadratic-weighted Cohen’s kappa $\kappa_{w}$	0.669 [0.565, 0.755]
Quadratic-weighted $\kappa_{w}$ , leave-one-week-out refit	0.661
Odour-report correlation, leave-one-week-out tier	$+0.698$
Unweighted Cohen’s kappa $\kappa$	0.397
Strict element-wise accuracy	0.757

Table S19: Headline performance of the meteorology-only multi-site Bayesian alert-tier classifier. All metrics evaluated on the synchronous Jan–Mar 2025 walk-forward window (

n=8{,}536

shared-grid 15-min timesteps; 13 weekly retrains per constituent nowcaster; Methods, “Multi-site Bayesian alert-tier classifier”). The predicted tier is constructed purely from meteorology: no measured target-species concentration is used as an input at inference time. Confidence intervals are block bootstrap (

B=1{,}000

resamples, 24-h block length) on the synchronous timeseries to accommodate within-episode autocorrelation. Per-tier P/R/F 1 values are paired with bootstrap 95% CIs in Supplementary Table S6 ; the full confusion matrix is in Supplementary Table S5 . The same-architecture vote-count baseline replaces the Bayesian accumulator with a hard count of latched per-channel activations and holds all other pipeline stages fixed. The

\Delta\kappa_{w}

interval and

p

-value are computed from a paired block bootstrap, in which the same resampled blocks are used for both estimators so that shared block-to-block variation cancels. An unpaired bootstrap, which resamples the two

\kappa

values independently, approximately triples the interval width and is not appropriate for two estimators evaluated on identical timesteps. The majority-class baseline is reported because the tier distribution is dominated by the Normal state, so strict accuracy alone does not evidence skill; the unweighted

\kappa

is reported alongside

\kappa_{w}

because quadratic weighting materially raises the reported agreement when most errors are off-by-one tier. External validation against community odour reports is fully held out: the odour-report record was not used in training, hysteresis selection or likelihood-ratio design. The leave-one-week-out figures quantify the fusion-parameter tuning optimism directly (

\Delta\kappa_{w}=0.008

); the constrained-ordering sensitivity is reported in Supplementary Note 6.

Figure S1: Co-located 15-minute time series of H 2 S and CH 4 at the principal receptor across the autumn 2024 walk-forward validation window. Top: H 2 S concentration with WHO Medium ( $2\,\mu\mathrm{g\,m^{-3}}$ ) and High ( $7\,\mu\mathrm{g\,m^{-3}}$ ) thresholds. Bottom: simultaneously measured CH 4 concentration on the class-boundary scale obtained by inverting the linear fit $\mathrm{H_{2}S}=5.55\,\mathrm{CH_{4}}-8.29$ (Low $<1.854$ , Medium $1.854$ – $2.756$ , High $\geq 2.756$ ppm). The strong concurrent coupling between the two species is the basis for the cross-species transfer experiment reported in main Fig. 6, panels b (right reliability diagram), c (CH 4 cross-correlogram with odour reports) and d (right panel: cross-model agreement $r=0.777$ ). Methods: “Cross-species CH 4 nowcaster”.

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Jul 26, 2026, cs.LGJ/K move · Enter open · S save

Physics-Informed Neural Networks for Predicting Nitrous Oxide Flux

Freddy Yu, Jashanjeet Kaur Dhaliwal, Subhadeep Chakraborty

Harvard University · Department of Biosystems Engineering and Soil Science University of Tennessee · Department of Mechanical and Aerospace Engineering University of Tennessee

Greenhouse Gas Soil Neural Network

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Nitrous oxide (N

_2

O) is the dominant ozone-depleting substance emitted in the 21st century, and the third largest contributor to anthropogenic greenhouse gases due to its high potency and long atmospheric lifetime, with more than 70% of N

_2

O emissions occurring as a result of agricultural processes. Current approaches to predicting N

_2

O flux emissions include process-based models such as DayCent and Cycles, as well as classical AI models, but the application of Physics-Informed Neural Networks (PINNs) to predicting N

_2

O flux emissions is largely underexplored. Our paper draws upon the mechanistic equations that underlie the DayCent family of process-based models to construct a rigorously derived, literature-traceable physics residual. We then build and train an MLP-based PINN on a multi-site agricultural dataset spanning four geographically distinct US agricultural sites. Across all tested values of the physics loss weighting hyperparameter

λ

, our PINN consistently and substantially outperformed uncalibrated Cycles simulation (R

^2=0.01

), with our MLP baseline achieving mean R

^2=0.411

across ten random seeds. Physics constraints consistently degrade model performance in holdout validation, with marginal degradation at low

λ

and significant degradation at high

λ

, but consistently improve model performance and reduce performance variability in leave-one-site-out validation. This suggests that physics constraints sacrifice in-distribution accuracy for out-of-distribution robustness, anchoring the model toward biogeochemically plausible behavior on unfamiliar soil conditions --- though cross-site generalization remains challenging, with negative R

^2

across all seeds and

λ

values on our geographically distinct held-out site.

Abstract

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