TopoFlow: Topography-aware Pollutant Flow Learning for High-Resolution Air Quality Prediction

Ammar Kheder; Helmi Toropainen; Wenqing Peng; Samuel Antão; Jia Chen; Michael Boy; Zhi-Song Liu

cs.LGFeb 18, 2026

TopoFlow: Topography-aware Pollutant Flow Learning for High-Resolution Air Quality Prediction

Authors: Ammar Kheder, Helmi Toropainen, Wenqing Peng, Samuel Antão, Jia Chen, Michael Boy, Zhi-Song Liu

Organizations: Department of Computational Engineering, Lappeenranta–Lahti University of Technology LUT, Finland · Atmospheric Modelling Centre Lahti, Lahti University Campus, Finland · Institute for Atmospheric and Earth System Research, University of Helsinki, P.O. Box 64, Helsinki 00014, Finland · Advanced Micro Devices (AMD), Munich, Germany · Technical University of Munich, Munich, Germany

Abstract

We propose TopoFlow (Topography-aware pollutant Flow learning), a physics-guided neural network for efficient, high-resolution air quality prediction. To explicitly embed physical processes into the learning framework, we identify two critical factors governing pollutant dynamics: topography and wind direction. Complex terrain can channel, block, and trap pollutants, while wind acts as a primary driver of their transport and dispersion. Building on these insights, TopoFlow leverages a vision transformer architecture with two novel mechanisms: topography-aware attention, which explicitly models terrain-induced flow patterns, and wind-guided patch reordering, which aligns spatial representations with prevailing wind directions. Trained on six years of high-resolution reanalysis data assimilating observations from over 1,400 surface monitoring stations across China, TopoFlow achieves a PM2.5 RMSE of 9.71 ug/m3, representing a 71-80% improvement over operational forecasting systems and a 13% improvement over state-of-the-art AI baselines. Forecast errors remain well below China's 24-hour air quality threshold of 75 ug/m3 (GB 3095-2012), enabling reliable discrimination between clean and polluted conditions. These performance gains are consistent across all four major pollutants and forecast lead times from 12 to 96 hours, demonstrating that principled integration of physical knowledge into neural networks can fundamentally advance air quality prediction.

Figures & tables

Figure 1: TopoFlow architecture for physics-guided air quality prediction. The model takes as input concentrations of six air pollutants, major meteorological data, population density, spatial coordinates, time stamps, and a topographic map, and outputs pollutant concentrations at lead times from 12 to 96 hours. All input data are stacked into a multi-layer 2D map, then cropped into non-overlapping patches. TopoFlow shuffles patch order based on the wind field within each sector, then processes patches through a Swin Transformer backbone. The topographic map introduces attention bias for topography-aware feature representation.

Figure 2: Overall performance of air pollution prediction. (a) , Ground truth (CAQRA reanalysis) PM 2.5 observations. (b) , TopoFlow PM 2.5 predictions. (c) , Prediction error ( $|\hat{y}-y|$ , where $\hat{y}$ is the model prediction and $y$ the CAQRA reanalysis) distribution across lead times comparing TopoFlow, ClimaX, and AirCast. Box plots indicate median (middle line), 25th and 75th percentile (box), and 5th and 95th percentile (whiskers). (d) , Spatial distribution of TopoFlow bias in Sichuan (with complex terrains), showing underestimation (blue) in the basin interior and overestimation (red) near elevated margins, consistent with residual difficulty in resolving sharp terrain-induced concentration gradients at the plateau-basin interface.

Figure 3: Forecast skill as a function of lead time for six air pollutants. RMSE validated against OpenAQ stations across China for 2019. a , PM 2.5 . b , PM 10 . c , NO 2 . d , SO 2 . e , CO. f , O 3 . TopoFlow (green) achieves the lowest errors for particulate matter and NO 2 . Aurora (purple) shows superior performance for O 3 and CO, which require three-dimensional atmospheric representation to capture stratospheric intrusions and vertical transport.

Figure 4: Seasonal PM 2.5 distribution from forecasts, reanalysis, and observations. (a–d) , CAMS forecasts. (e–h) , Aurora predictions. (i–l) , CAQRA reanalysis. (m–p) , TopoFlow predictions. (q–t) , OpenAQ measurements. Columns: Winter (15 January 2019), Spring (1 March 2019), Summer (12 July 2019), Autumn (19 October 2019). TopoFlow achieves lowest RMSE (25.9 $\mu$ g/m 3 ) against independent stations, outperforming CAQRA (37.0 $\mu$ g/m 3 ), CAMS (44.1 $\mu$ g/m 3 ), and Aurora (49.8 $\mu$ g/m 3 ). Relative to China’s 24-hour PM 2.5 threshold of 75 $\mu$ g/m 3 (GB 3095-2012) [ 7 ] , only TopoFlow and CAQRA maintain errors below 50% of the regulatory limit.

Figure 5: Topographic blocking in Sichuan Basin. (a) , CAQRA (ground truth) PM 2.5 distribution across China at 7 July 2018, 20:00 UTC, with the study region marked by the green box. (b) , CAQRA (ground truth) PM 2.5 concentrations and wind vectors at forecast time (8 July 2018, 08:00 UTC) within the Sichuan Basin. The green line indicates 30.0°N transect. (c) , TopoFlow 12-hour prediction achieving spatial correlation r = 0.90. (d) , West-east transect along 30.0°N comparing CAQRA (black), TopoFlow (red), AirCast (orange dashed), and ClimaX (blue dotted) against elevation profile (gray shading). Inset table reports the terrain-induced concentration gradient

\Delta=C_{\text{basin,max}}-C_{\text{plateau,min}}

for each model. (e) , Schematic of topographic blocking mechanism: the Tibetan Plateau blocks westerly winds, trapping pollutants within the basin.

Figure 6: November 2018 Beijing haze episode. (a) , Seven-day back-trajectory arriving at Beijing on 14 November 2018, adapted from FLEXPART-SOSAA analysis in Foreback et al. [ 37 ] . The trajectory originates from Central Asia and passes through the Xinjiang region before traversing Hebei province and arriving at Beijing. Dates along the trajectory indicate the air mass position at daily intervals from 8 to 14 November. (b) , TopoFlow-predicted PM 2.5 concentration fields on 10, 12, 14, and 16 November 2018 with ERA5 wind vectors overlaid. Beijing is marked with a star. The sequence shows the progressive buildup of pollution across northern China during the episode (10–14 November) and the rapid clearing on 16 November following the passage of a clean northwesterly air mass.

Figure 7: Physics-guided attention learns terrain-aware transport patterns. (a–c) , Attention weight matrices over the Tianshan mountain region (elevation 26–5698 m): Baseline ( a ), Baseline + wind-guided patch reordering ( b ), and Baseline + wind-guided patch reordering + elevation bias (TopoFlow) ( c ). Vertical stripes in ( a ) indicate shortcut-like routing through globally informative patches; wind-guided reordering in ( b ) redistributes attention along advective transport pathways; elevation bias in ( c ) further modulates attention to respect topographic barriers. (d–f) , Corresponding attention weight distributions with mean values $\mu$ : the baseline ( d , $\mu{=}0.44$ ) shows a broad, left-skewed distribution; wind-guided reordering ( e , $\mu{=}0.48$ ) concentrates weights into a narrower, higher-mean peak; the full TopoFlow model ( f , $\mu{=}0.46$ ) produces a bimodal-like distribution reflecting selective suppression of cross-barrier attention. (g) , Training convergence: TopoFlow achieves 5.7% lower final validation loss (0.249 vs. 0.264). The fine-tuning phase (dashed vertical line, $\alpha$ reset) triggers a distinct drop from 0.257 to 0.249, indicating that re-calibrating the elevation penalty after initial convergence provides an additional optimization degree of freedom absent in the baseline. Shaded regions indicate checkpoint variance.

Figure 8: Multi-pollutant model comparison over the Sichuan Basin (8 July 2018, 08:00 UTC, 12h forecast). Rows: PM 2.5 , PM 10 , SO 2 , NO 2 , CO, O 3 . Columns: CAQRA observations, TopoFlow, CAMS reanalysis, Aurora. All fields at 0.4 ∘ . $R$ and RMSE computed against CAQRA.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1: TopoFlow PM 2.5 forecast performance across lead times. a–d , CAQRA reanalysis (ground truth) for 12h, 24h, 48h, and 96h horizons. e–h , Corresponding TopoFlow predictions. i–l , Spatial bias maps showing prediction minus observation (blue: underestimation, red: overestimation). m–p , Scatter plots of predicted versus observed PM 2.5 concentrations with correlation coefficient $r$ and RMSE. Performance degrades gracefully from $r=0.79$ at 12h to $r=0.60$ at 96h, with RMSE increasing from 8.2 to 11.0 $\mu$ g/m 3 .

Meteorological fields
Variable	Symbol	Units	Source	Resolution	Normalization
Zonal wind	$u$	m/s	CAQRA	0.25°	z-score
Meridional wind	$v$	m/s	CAQRA	0.25°	z-score
Temperature	$T$	K	CAQRA	0.25°	z-score
Relative humidity	RH	%	CAQRA	0.25°	z-score
Surface pressure	$p_{s}$	hPa	CAQRA	0.25°	z-score

Appendix

Table S1: Complete specification of TopoFlow input variables.

Model	Type	Parameters	Training Data	Reference
Aurora	AI foundation model	1.3B	ERA5 + CAMS	Bodnar et al. (Nature 2025)
ClimaX baseline	Climate foundation model	100M	CAQRA	Nguyen et al. (ICML 2023)
AirCast	Deep learning	50M	CAQRA	Nedungadi et al. (ICML WS 2025)
CAMS	Numerical CTM	–	ECMWF IFS + emissions	Inness et al. (ACP 2019)
CUACE	Numerical CTM	–	CMA + MEIC emissions	Dai et al. (2019)
TopoFlow (Ours)	Physics-guided ViT	52.5M	CAQRA	This work

Appendix

Table S2: Baseline model specifications and training details. ClimaX baseline and AirCast were trained on CAQRA for fair comparison.

Category	Parameter	Value
Architecture	Patch size $p$	2
	Embedding dimension $d$	768
	Number of transformer layers $L$	12
	Number of attention heads	8
	MLP hidden dimension	3072
	Dropout rate	0.1

Appendix

Table S3: Complete hyperparameter configuration for TopoFlow training.

Temporal Horizon	Seasonal Distribution				Daily Distribution				Day of Month Distribution			Total Samples
Temporal Horizon	Winter (Jan-Mar)	Spring (Apr-Jun)	Summer (Jul-Sep)	Autumn (Oct-Dec)	Night (00:00-06:00)	Morning (06:00-12:00)	Afternoon (12:00-18:00)	Evening (18:00-24:00)	Days 1-10	Days 11-20	Days 21-31	Total Samples
12h	255	262	245	238	234	270	227	269	338	329	333	1,000
24h	246	225	268	261	266	227	250	257	332	327	341	1,000
48h	252	254	278	216	260	233	273	234	342	311	347	1,000
96h	255	257	239	249	272	232	254	242	344	331	325	1,000
Total	1,008	998	1,030	964	1,032	962	1,004	1,002	1,356	1,298	1,346	4,000

Appendix

Table S4: Test set evaluation sample distribution across temporal dimensions (year 2018). Each forecast horizon contains 1,000 stratified samples covering all seasons, times of day, and days of the month.

Pollutant	Model	12h	24h	48h	96h	Average
PM 2.5	TopoFlow (Ours)	8.18	9.66	9.96	11.03	9.71
	ClimaX baseline	9.41	11.11	11.45	12.68	11.16
	AirCast	10.72	12.67	12.21	13.40	12.25
PM 10	TopoFlow (Ours)	14.78	17.06	17.70	19.45	17.25
	ClimaX baseline	17.00	19.62	20.36	22.37	19.84
	AirCast	17.90	20.29	19.85	21.63	19.92

Appendix

Table S5: RMSE performance by pollutant and forecast horizon (Test Set 2018). All units in

\mu

g/m 3 . Bold indicates best performance. All models were evaluated against CAQRA reanalysis.

Pollutant	Model	12h	24h	48h	96h	Average	$\downarrow$ %
PM 2.5	TopoFlow (Ours)	26.9	27.1	28.0	29.9	28.0	–
	ClimaX baseline	30.4	30.6	31.6	33.8	31.6	+13%
	AirCast	31.5	31.7	32.8	35.0	32.8	+17%
	Aurora	33.2	31.2	35.1	41.1	35.2	+26%
	CUACE †	–	34–48	–	–	41.0	+46%
	CAMS ‡	52.7	53.2	54.3	56.8	54.3	+94%

Appendix

Table S6: Validation Against Independent Ground Stations (2019). RMSE in

\mu

g/m 3 . Green = TopoFlow (Ours). Bold = best per lead time.

\downarrow

% = relative increase vs. best model.

Pollutant	Threshold	TopoFlow	ClimaX	AirCast	Aurora	CAMS
PM 2.5	75 $\mu$ g/m 3	28.0 (37%)	31.6 (42%)	32.8 (44%)	35.2 (47%)	54.3 (72%)
PM 10	150 $\mu$ g/m 3	48.8 (33%)	55.1 (37%)	57.1 (38%)	63.3 (42%)	78.6 (52%)
NO 2	80 $\mu$ g/m 3	23.9 (30%)	27.0 (34%)	28.0 (35%)	23.9 (30%)	30.0 (38%)
SO 2	150 $\mu$ g/m 3	13.3 (9%)	15.0 (10%)	15.5 (10%)	21.4 (14%)	83.3 (56%)
CO ∗	4 mg/m 3	0.60 (15%)	0.68 (17%)	0.70 (18%)	0.59 (15%)	0.61 (15%)
O 3	160 $\mu$ g/m 3	76.7 (48%)	86.7 (54%)	–	57.9 (36%)	73.2 (46%)

Appendix

Table S7: Forecast errors relative to China’s regulatory air quality thresholds (GB 3095-2012, Class II, 24-hour average). RMSE from independent OpenAQ validation (2019). Values in parentheses indicate RMSE as a percentage of the regulatory threshold. Shaded cells indicate errors exceeding 50% of the threshold, limiting operational utility for regulatory decision-making.

Tiling Strategy	Wind Calculation	Val Loss	$\Delta$ Loss
Global wind direction	Single vector (country-wide)	0.309	—
Coarse tiling	$2{\times}2$ tiles	0.295	$-$ 0.014
	$4{\times}4$ tiles	0.293	$-$ 0.016
Medium tiling	$8{\times}8$ tiles	0.291	$-$ 0.018
	$12{\times}12$ tiles	0.288	$-$ 0.021
	$16{\times}16$ tiles	0.280	$-$ 0.029

Appendix

Table S8: Tile granularity optimization for wind-guided reordering. Validation loss on 2017 holdout set.

Model	Scanning	Wind Tiles	Elevation $\alpha$	Val Loss
ClimaX baseline	Row-major	×	×	0.264
+ Wind-guided reordering	Wind-directed	$32{\times}32$	×	0.257
+ Topography-aware attention bias (TopoFlow)	Wind-directed	$32{\times}32$	✓	0.249

Appendix

Table S9: Component contribution analysis using optimal

32{\times}32

tiles.

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Accurate air quality forecasting is crucial for protecting public health and guiding environmental policy, yet it remains challenging due to nonlinear spatiotemporal dynamics, wind-driven transport, and distribution shifts across regions. Physics-based models are interpretable but computationally expensive and often rely on restrictive assumptions, whereas purely data-driven models can be accurate but may lack robustness and calibrated uncertainty. To address these limitations, we propose Neural Dynamic Diffusion-Advection Fields (NeuroDDAF), a physics-informed forecasting framework that unifies neural representation learning with open-system transport modeling. NeuroDDAF integrates (i) a GRU-Graph Attention encoder to capture temporal dynamics and wind-aware spatial interactions, (ii) a Fourier-domain diffusion-advection module with learnable residuals, (iii) a wind-modulated latent Neural ODE to model continuous-time evolution under time-varying connectivity, and (iv) an evidential fusion mechanism that adaptively combines physics-guided and neural forecasts while quantifying uncertainty. Experiments on four urban datasets (Beijing, Shenzhen, Tianjin, and Ancona) across 1-3 day horizons show that NeuroDDAF consistently outperforms strong baselines, including AirPhyNet, achieving up to 9.7% reduction in RMSE and 9.4% reduction in MAE on long-term forecasts. On the Beijing dataset, NeuroDDAF attains an RMSE of 41.63

μ

g/m

^3

for 1-day prediction and 48.88

μ

g/m

^3

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