the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Jul 2026
Physics-constrained inverse neural estimation (PINE) of daily NOx emissions from TROPOMI NO2 columns over the North China Plain
Abstract. Daily-resolution NOx emissions are pivotal for air-quality forecasting, yet static inventories cannot capture day-to-day variability, and conventional satellite inversions are either computationally prohibitive (4D-Var) or circularly dependent on pre-existing emission products. We introduce physics-constrained inverse neural estimation (PINE), instantiated for NOx as PINE-NOx, which retrieves daily NOx emissions over the North China Plain (0.1°, 364 days of 2023) from Sentinel-5P/TROPOMI NO₂ columns. PINE is a physics-constrained autoencoder: a neural encoder maps observed columns to emissions, which a fixed, differentiable transport–chemistry operator decodes back into columns. Physics thus enters structurally through this decoder, not as a soft residual penalty; trained end-to-end to reconstruct observations without emission labels. On 80 season-balanced validation days, PINE-NOx-inferred emissions raise the log-space spatial correlation between simulated and observed columns from 0.395 to 0.837 (Δr = +0.442, p < 0.001), robustly across four encoder backbones and all four seasons. Two independent checks corroborate the inversion: an independent WRF-Chem simulation cuts the summer column bias from +113 % to +5 %, and the recovered seasonal cycle agrees with the fully independent, bottom-up MEIC inventory (r = 0.68), while a prior-removal experiment confirms that the spatial pattern originates from the observations rather than the prior. The inventory provides the daily-resolved dynamics of North China Plain NOx emissions, a physically disaggregated emission winter/summer ratio of ~1.4, and ~11 % spatial redistribution relative to EDGAR. PINE-NOx offers a physically interpretable, label-free and computationally inexpensive paradigm for atmospheric emission inversion.
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Status: open (until 16 Aug 2026)
- CC1: 'Comment on egusphere-2026-3233', Nima Zafarmomen, 05 Jul 2026 reply
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RC1: 'Comment on egusphere-2026-3233', Anonymous Referee #1, 24 Jul 2026
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This manuscript presents a physics-constrained inverse neural estimation framework, PINE-NOx, for retrieving daily NOx emissions over the North China Plain from TROPOMI NO2 columns. The topic is timely and relevant, and the idea of embedding a differentiable transport-chemistry operator as a fixed decoder within an autoencoder is innovative. The manuscript is generally well structured and includes several useful diagnostic experiments, including encoder-backbone comparison, prior-removal tests, WRF-Chem evaluation, MEIC comparison, and chemical-lifetime sensitivity analysis. However, several important issues remain regarding absolute-emission identifiability, prior dependence, and validation independence. Addressing these concerns would substantially strengthen the manuscript and improve its suitability for publication.
Major Comments:
The manuscript states that PINE-NOx retrieves daily NOx emissions, but Section 2.5 clearly indicates that the domain-wide annual total is normalized to EDGAR. The Abstract should explicitly mention that the final PINE-NOx emissions are normalized to the EDGAR annual total. Without this clarification, readers may interpret the absolute emission magnitude as being independently constrained by TROPOMI, whereas the satellite observations mainly constrain spatial redistribution and temporal variability. “….. PINE-NOx retrieves daily spatial-temporal emission adjustments constrained by TROPOMI, with the annual total normalized to EDGAR.”
The manuscript normalizes the domain-wide annual total emission to EDGAR, but the rationale for choosing EDGAR rather than MEIC is not sufficiently justified. Since MEIC is available as an independent bottom-up inventory and has a lower annual total than EDGAR, the choice of EDGAR directly affects the absolute magnitude of the final emissions. The authors should explain why EDGAR is selected as the normalization target and provide a sensitivity test using MEIC-based or alternative annual-total normalization. This is particularly important because the manuscript notes that the static EDGAR 2022 inventory may not fully reflect the continued decline of NOx emissions over the North China Plain in 2023.
In Figure 11(c), the interpretation of relative differences in clean peripheral regions requires further clarification. EDGAR emissions in these regions may be extremely small or even zero, but such low values do not necessarily indicate truly negligible emissions; they may also reflect limited activity statistics or spatial allocation uncertainty in the inventory. If these grids are included in the inversion, Huber prior regularization, or annual-total normalization, the authors should clarify whether any minimum emission threshold or floor value was applied, and how relative differences were calculated for near-zero EDGAR values. A short discussion of whether low-prior grids are physically meaningful, inventory-limited, or excluded from quantitative interpretation would improve the robustness of the spatial redistribution analysis. Relevant studies that discuss low-prior emissions, prior-related uncertainty, and uncertainty-aware satellite-based NOx emission inversions may also be cited, including but not limited to:
https://doi.org/10.1088/1748-9326/ac48b4
https://doi.org/10.1016/j.rse.2023.113720
https://doi.org/10.1016/j.rse.2023.113917
https://doi.org/10.5194/acp-25-2291-2025
https://doi.org/10.5194/essd-17-3329-2025
The manuscript reports “about 11% spatial redistribution relative to EDGAR”, but the metric is not clearly defined. Since the domain-wide annual total is normalized to EDGAR, this redistribution should also be quantified explicitly. The authors should define how the 11% value is calculated, for example whether it represents a mean absolute grid difference, an L1 redistribution fraction, or another metric. It would also be helpful to discuss whether enhanced low emissions indicate possible missing or misallocated sources in EDGAR, or simply reflect redistribution under the EDGAR-normalized total constraint.
The manuscript should more carefully distinguish between internal reconstruction skill and external model-consistency evaluation. For example, the Abstract states that “two independent checks corroborate the inversion,” and Section 3.1 refers to external checks provided by the independent WRF-Chem simulation. However, the forward reconstruction skill is an internal consistency metric because it uses the same differentiable decoder and TROPOMI NO2 observations as in training. The WRF-Chem experiment is independent in terms of the transport-chemistry model, but it is still evaluated against the same TROPOMI NO2 observations used in the inversion. Therefore, it should be described as an external CTM-based consistency check rather than fully independent validation of the emissions. The Abstract, Section 3.1, and Conclusions should be revised accordingly to avoid overclaiming validation independence.
If the authors wish to claim independent emission validation, they should consider using observational datasets that do not enter the inversion, such as CEMS measurements, ground-based NO2 observations, aircraft/mobile measurements, or facility-level emission records. Relevant examples include, but are not limited to:
https://doi.org/10.1021/acs.est.9b04488
https://doi.org/10.5194/acp-22-10875-2022
https://doi.org/10.5194/acp-23-8001-2023
https://doi.org/10.1109/TGRS.2025.3620116
https://doi.org/10.5194/acp-26-4405-2026
In Table 1 (“Magnitude treatment”), Section 2.4 (lines 207-220), and Section 2.5 (lines 230-244): Since the rendering loss removes the domain-wide mean, it is unclear how domain-mean daily emission variability is constrained by observations. Please clarify how this domain-mean temporal variability is constrained under a demeaned loss formulation. Is it derived from TROPOMI spatial-pattern changes, meteorological inputs, prior regularization, annual-total normalization, or the neural-network architecture?
Minor Comments:
In Section 3.3 and the caption of Figure 11, the interpretation of the spatial redistribution seems appear inconsistent. The text describes a “downward adjustment in pollution cores and an upward adjustment in clean peripheral regions”, whereas the caption states the opposite “….. enhanced emissions in the pollution cores (red) and reduced emissions in the clean periphery (blue)”. Please check Figure 11(c) and revise the text or caption accordingly.
In Figure 11(c), the relative difference appears to be saturated over large areas, especially in red, under the current 60% color scale. Please justify the choice of this range or provide an additional unsaturated or percentile-based version to better show spatial variability.
Citation: https://doi.org/10.5194/egusphere-2026-3233-RC1
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The manuscript presents a physics-constrained neural inversion framework, PINE-NOx, for estimating daily NOx emissions over the North China Plain from TROPOMI NO₂ satellite columns. The method uses a neural encoder to infer emissions and a fixed differentiable transport–chemistry decoder to reconstruct NO₂ columns, allowing label-free training without using existing emission products as direct supervision. The authors report that PINE-NOx improves the spatial correlation between simulated and observed NO₂ columns from 0.395 using EDGAR to 0.837, and an independent WRF-Chem evaluation reduces summer column bias from +113% to +5%. The study is technically interesting and relevant for high-temporal-resolution emission inversion, air-quality forecasting, and satellite-based atmospheric composition analysis.