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
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 ( ∣y^−y∣ , where 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 μ g/m 3 ) against independent stations, outperforming CAQRA (37.0 μ g/m 3 ), CAMS (44.1 μ g/m 3 ), and Aurora (49.8 μ g/m 3 ). Relative to China’s 24-hour PM 2.5 threshold of 75 μ 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 Δ=Cbasin,max−Cplateau,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 μ : the baseline ( d , μ=0.44 ) shows a broad, left-skewed distribution; wind-guided reordering ( e , μ=0.48 ) concentrates weights into a narrower, higher-mean peak; the full TopoFlow model ( f , μ=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, α 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 μ g/m 3 .
Variable
Symbol
Units
Source
Resolution
Normalization
Meteorological fields
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
ps
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
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
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 μ g/m 3 . Bold indicates best performance. All models were evaluated against CAQRA reanalysis.
Pollutant
Model
12h
24h
48h
96h
Average
↓ %
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 μ g/m 3 . Green = TopoFlow (Ours). Bold = best per lead time. ↓ % = relative increase vs. best model.
Pollutant
Threshold
TopoFlow
ClimaX
AirCast
Aurora
CAMS
PM 2.5
75 μ g/m 3
28.0 (37%)
31.6 (42%)
32.8 (44%)
35.2 (47%)
54.3 (72%)
PM 10
150 μ g/m 3
48.8 (33%)
55.1 (37%)
57.1 (38%)
63.3 (42%)
78.6 (52%)
NO 2
80 μ g/m 3
23.9 (30%)
27.0 (34%)
28.0 (35%)
23.9 (30%)
30.0 (38%)
SO 2
150 μ 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 μ 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
Δ Loss
Global wind direction
Single vector (country-wide)
0.309
—
Coarse tiling
2×2 tiles
0.295
− 0.014
4×4 tiles
0.293
− 0.016
Medium tiling
8×8 tiles
0.291
− 0.018
12×12 tiles
0.288
− 0.021
16×16 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 α
Val Loss
ClimaX baseline
Row-major
×
×
0.264
+ Wind-guided reordering
Wind-directed
32×32
×
0.257
+ Topography-aware attention bias (TopoFlow)
Wind-directed
32×32
✓
0.249
Appendix
Table S9: Component contribution analysis using optimal 32×32 tiles.
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 μg/m3 for 1-day prediction and 48.88 μg/m3 for 3-day prediction, representing the best performance among all compared methods. In addition, NeuroDDAF improves cross-city generalization and yields well-calibrated uncertainty estimates, as confirmed by ensemble variance analysis and case studies under varying wind conditions.
Accurate air quality forecasting is essential for public health and urban environmental management, but remains challenging because pollutant channels differ in periodicity and distribution drift, while their concentration trajectories contain both multi-scale dependencies and rapid changes. Recent methods have improved spatial dependency learning and meteorological covariate modeling. However, pollutant channels are still passed through the same normalization rule and temporal backbone, using a shared latent representation for channel-specific distributions and changes at different rates. To address this limitation, we propose AirFlow, a pollutant-aware dual-stream framework that operates on station multivariate observations without additional graph propagation or predefined signal decomposition. Specifically, AirFlow designs two novel blocks: (1) a statistic-guided normalization routing mechanism that selects a normalization path for each pollutant according to its 24-hour autocorrelation and distribution drift; and (2) a hierarchical dual-stream state model that combines multi-scale state space propagation with learnable response coefficients, where gated bidirectional cross-attention exchanges information and adaptively fuses the resulting representations. Experiments on real-world data from multiple cities show that AirFlow achieves the best performance in 34 of 36 metrics comparisons, with reductions of up to 11.11% root mean square error over the state-of-the-art baseline. AirFlow also requires only 0.0483M parameters and 0.0215G FLOPs, achieving high forecasting accuracy with low computational overhead.
Fan Yang, Nan Chen, Yijie Dong +2
School of Software Technology, Zhejiang University Hangzhou, Zhejiang 310000, China
Accurate air quality forecasting is essential for public health and environmental sustainability, but remains challenging due to the complex pollutant dynamics. Existing deep learning methods often model pollutant dynamics as an instantaneous process, overlooking the intrinsic delays in pollutant propagation. Thus, we propose AirDDE, the first neural delay differential equation framework in this task that integrates delay modeling into a continuous-time pollutant evolution under physical guidance. Specifically, two novel components are introduced: (1) a memory-augmented attention module that retrieves globally and locally historical features, which can adaptively capture delay effects modulated by multifactor data; and (2) a physics-guided delay evolving function, grounded in the diffusion-advection equation, that models diffusion, delayed advection, and source/sink terms, which can capture delay-aware pollutant accumulation patterns with physical plausibility. Extensive experiments on three real-world datasets demonstrate that AirDDE achieves the state-of-the-art forecasting performance with an average MAE reduction of 8.79% over the best baselines. The code is available at https://github.com/w2obin/airdde-aaai.
Binqing Wu, Zongjiang Shang, Shiyu Liu +3
State Key Laboratory of Blockchain and Data Security, Zhejiang University · College of Computer Science and Technology, Zhejiang University · State Key Laboratory of Clean Energy Utilization, Zhejiang University