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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- CC1: 'Comment on egusphere-2026-3233', Nima Zafarmomen, 05 Jul 2026
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RC1: 'Comment on egusphere-2026-3233', Anonymous Referee #1, 24 Jul 2026
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 -
RC2: 'Comment on egusphere-2026-3233', Anonymous Referee #2, 20 Sep 2026
This manuscript presents a potentially useful idea that an amortized neural inversion in which an emission field inferred by an encoder is passed through a differentiable transport-decay operator and trained against TROPOMI NO2 columns. The effort to discuss identifiability, compare several encoder architectures, conduct ablation experiments, and state that the absolute emission magnitude remains prior-dependent is appreciated. The topic is relevant to ACP, and a computationally efficient inversion method could be valuable. However, further evidence would help establish the accuracy of the PINE-derived daily NOx emissions. The principal validation metric assesses reconstruction of the TROPOMI field that is also supplied to the encoder, while the WRF-Chem results are compared with the same TROPOMI observations used in the inversion. These evaluations provide useful evidence of reconstruction skill and consistency across modelling approaches, although their independence is limited. Additional clarification and sensitivity analyses regarding the decoder assumptions, treatment of missing or non-positive observations, EDGAR-based absolute scaling, and uncertainty estimation would further strengthen confidence in the inferred emissions. I therefore recommend major revision.Major comments:1. The encoder receives the demeaned log TROPOMI VCD as an input and is trained to reconstruct that same VCD after passage through the decoder (Sect. 2.3). The reported held-out skill of `r = 0.837` therefore measures how well an autoencoder reconstructs its own input on unseen days. Holding out days or seasons from weight optimization does not make the target independent, because the complete VCD field for each validation day is still supplied to the encoder at inference time. With millions of trainable parameters and only 284 training days, a high reconstruction correlation does not demonstrate that the latent emission field is correct or uniquely identified. The manuscript should clearly distinguish observation reconstruction, forward-model consistency, and emission validation.2. The decoder starts from a zero column, integrates for about 4 h, uses daytime-mean 10 m winds, represents chemistry with a spatially uniform monthly lifetime, treats boundary inflow as a domain-wide scalar, and apparently converts a NOx emission flux directly into an NO2 column. This is not an “exact numerical solver” of NOx-NO2 transport and chemistry, and passing emissions through this operator does not by itself fully establish the physical reliability of the inferred emissions.3. The manuscript acknowledges the temporal sampling problem in Sect. 4.3, but still repeatedly describes the output as a daily emission inventory and interprets a day-to-day coefficient of variation of 29%. A 13:30 snapshot constrains an effective emission state over a limited preceding period, conditional on assumed lifetime and transport. It does not uniquely determine a 24 h mean emission flux or its diurnal profile. A lag-1 autocorrelation of 0.249 is not evidence that the remaining variability is genuine emission variability, because retrieval errors, clouds, sampling, and meteorology are themselves temporally correlated. The authors should either provide validation showing that the retrieved quantity represents daily mean emissions or rename and reinterpret it as an overpass-time effective emission estimate.4. The WRF-Chem experiment needs a complete reproducible configuration, including model version, domain and vertical grid, meteorological forcing and nudging, spin-up treatment, anthropogenic temporal profiles, biogenic and lightning emissions, boundary conditions, chemical initial conditions, model-to-satellite sampling, vertical interpolation, cloud screening, and the exact use of daily PINE emissions.5. The reported overall uncertainty of 12-15% is not derived transparently. Neural cross-fold spread is only one component and is not a substitute for uncertainty from the TROPOMI retrieval, sampling and clouds, background subtraction, transport winds, chemical lifetime, initial and boundary conditions, regularization strengths, EDGAR total, network initialization, and structural model error. A robust uncertainty assessment should propagate these sources to daily, monthly, grid-cell, and domain-total emissions.Minor comments1. The terms “physics-constrained”, “hard constraint”, “physical self-consistency”, and “validated” are used too strongly.2. Lines 286-293 infer “year-round extrapolation” from a seasonally balanced random split. Interleaved holdout is interpolation in time, not year-round extrapolation. Even the leave-one-season-out test remains reconstruction of the input VCD.3. The definition and derivation of the monthly lifetime values should be given in the Methods, including the interpolation formula and supporting literature. The selection of `E_eff/R = 3000 K` also requires justification.4. State whether `Tg` refers to Tg NO2, Tg NOx expressed as NO2, or Tg N, and use the same convention for EDGAR, MEIC, and PINE.5. Remove or revise the policy implication that annual inventories underestimate winter health-exposure risk. Emissions alone do not determine exposure, and the inferred winter enhancement is sensitive to the assumed chemical lifetime.Citation: https://doi.org/
10.5194/egusphere-2026-3233-RC2
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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.