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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Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2026-3233', Nima Zafarmomen, 05 Jul 2026
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AC1: 'Reply on CC1', Yinan Wang, 27 Oct 2026
We thank N. Zafarmomen for the interest in our work and for a constructive comment. Several of the points concern what the satellite columns can and cannot determine in this framework, and we have tried to answer them by explaining the reasoning behind the design and the tests that support it.
General comment
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.
Thank you for the summary. Two aspects of it deserve a clarification, because they bear on how the results should be read.
First, the quantity that the satellite constrains is the spatial pattern of the emissions, not their daily amount. The training loss compares simulated and observed columns after removing the domain mean of their logarithms, so any change of the domain-wide emission level leaves the loss unchanged. The revised title therefore speaks of "emission spatial patterns", and the products are annual and monthly patterns. The daily fields are effective emissions at the overpass time (about 13:30 local time); a single overpass does not determine a 24 h mean emission rate.
Second, a reduction of the domain-mean column bias in WRF-Chem is not evidence for the inversion. The domain total of PINE-NOx is fixed by the normalization to EDGAR, so a change of the mean bias reflects that design choice and the configuration of the chemical model rather than information from the satellite. In the revised WRF-Chem experiment all runs have the same NOx total inside the domain and differ only in the spatial pattern of the emissions, and the comparison is made on the pattern of the simulated columns and of surface NO2 (Sect. 3.2).
Comment 1
The manuscript should more clearly distinguish between internal physical self-consistency and fully independent validation. Much of the reported improvement is based on the same differentiable decoder used during training, while the WRF-Chem test still uses TROPOMI NO₂ as the comparison reference. The authors should clarify the degree of independence of each validation step.
We agree, and the revised manuscript states the independence of each test where it is reported. The table summarizes the four kinds of evidence.
Test
Shares with the inversion
What it can show
Reconstruction of the TROPOMI columns (Sect. 3.1)
the decoder and the observations
internal consistency; not a validation of the emissions
WRF-Chem columns against TROPOMI (Sect. 3.2)
the observations only
consistency with the fitted observations in an independent transport and chemistry model
WRF-Chem surface NO2 against 160 CNEMC stations (Sect. 3.2)
nothing
an independent test; in July 2023 it does not show the PINE-NOx pattern to be better than EDGAR
MEIC 2023 inventory (Sect. 3.3)
nothing
consistency with an independent bottom-up estimate; the PINE-NOx pattern is closer to MEIC than EDGAR is, clearly in July and not in January once a synthetic test with known emissions is taken into account (Sect. 3.3)
None of these tests is a complete validation of the emissions. The station comparison is the only observational test independent of the satellite, and its result is reported as it is; compared directly with the emissions in the station cells, the station NO2 also correlates slightly better with EDGAR than with PINE-NOx (log-space r = 0.365 against 0.306; Sect. 3.2, Fig. S6). An inventory comparison is informative but cannot decide which allocation is right, since MEIC has its own errors. Facility-level or flux observations would be needed for that, and the manuscript says so in Sect. 4.3. A synthetic test with known emissions, added in the revision, also shows that the method by itself produces a change of the pattern relative to EDGAR of about the size retrieved from the observations, so its size is no longer reported as an observed redistribution (Sect. 3.3).
Comment 2
The treatment of absolute emission magnitude needs further explanation. Since the rendering loss is demeaned and the annual total is normalized to EDGAR, the observations mainly constrain spatial patterns and temporal variability rather than absolute emissions. This limitation should be emphasized more clearly in the abstract, results, and conclusion.
We agree that the absolute magnitude is not constrained, and the abstract, Sect. 2.4, Sect. 2.5, Sect. 4.3 and the Conclusions now state this. One part of the comment needs a correction: the observations do not constrain the temporal variability of the domain-wide emissions either. Multiplying all emissions of a given day by a constant shifts the logarithm of the simulated column by a constant, which the demeaned loss removes. The same argument applies to every day separately, so neither the annual level nor its day-to-day or month-to-month variation is seen by the loss. What the satellite does constrain is how the emissions of a day are distributed in space, and averaged over the year, how the distribution differs from EDGAR.
For this reason the revised paper reports no domain-level variability. The monthly totals of the product follow the EDGAR monthly profile, so that the annual and monthly totals come from one inventory, and the domain annual total can be rescaled to another inventory (for example MEIC, 0.88 of the EDGAR total) without changing any pattern, share or correlation in the paper.
Comment 3
The chemical lifetime parameterization is central to the inversion framework. Although the authors provide sensitivity tests, the use of monthly scalar lifetimes may oversimplify spatial variability in photochemistry, boundary-layer conditions, and NOx chemical regimes. A more explicit discussion of how this assumption affects regional emission estimates would strengthen the manuscript.
The point is well taken, and it helps to separate two ways in which the lifetime enters. Under near steady state the column scales roughly with the product of emission and lifetime. A lifetime error that is uniform over the domain therefore changes all columns by approximately a common factor, which the demeaned loss removes (it also changes the length of the plumes, a smaller effect that the tests below include); it affects the regional level and the seasonal amplitude of the emissions, which the inversion does not report, but not their spatial pattern. Only spatial differences in the lifetime can be mistaken for spatial differences in the emissions.
We tested both by retraining the model with eight variants of the lifetime table (scaled by 0.7 and 1.3, without its seasonal cycle, with the winter months scaled by 0.67 and 1.5, with a seasonal shape following the O(1D) photolysis frequency with and without its latitude dependence, and with a spatial lifetime pattern diagnosed from a WRF-Chem simulation with full chemistry; Sect. 4.1). Across these variants the annual emission shares change by 1.4 % at 0.5° (1σ, emission-weighted), and the share of the 10 % highest-emitting cells changes by at most 2 percentage points, small compared with the difference of about 23 percentage points between PINE-NOx and EDGAR (58.6 % against 35.2 %), although a synthetic test with known emissions (Sect. 3.3) shows that a difference of that size also arises from the method itself. This term is part of the uncertainty budget (Fig. 9).
The seasonal amplitude is a different matter. The winter-to-summer ratio of the emissions implied by the columns ranges from 1.1 to 1.8 when the winter lifetime is changed by ±25 % (Sect. 3.3 and Fig. S12), so it cannot be determined in this way and is not reported as a result. Nonlinear chemical regimes are not represented by a first-order decay, and Sect. 2.2 now lists this among the simplifications of the decoder.
Comment 4
The use of ERA5 10 m winds to approximate column transport should be better justified. Since NO₂ columns reflect transport through the boundary layer and lower troposphere, the authors should discuss the potential implications of using near-surface winds rather than vertically resolved or PBL-weighted winds.
We agree that the column is transported by winds through the boundary layer, which are usually stronger than the 10 m wind and may turn with height. To quantify the effect, we retrained the model with the ERA5 100 m wind and with the boundary-layer mean wind in place of the 10 m wind. Across the three wind levels the annual emission shares differ by about 1 % at 0.5° and 3 % at 0.1° (1σ, emission-weighted), one of the smaller terms of the uncertainty budget (Fig. 9, Sect. 4.3).
Transport itself does matter: switching advection off lowers the reconstruction correlation from 0.871 to 0.778 (Sect. 4.1). We think the sensitivity to the wind level is small mainly because the annual pattern averages over many days with different wind directions and speeds, so that a systematic difference in wind speed changes the displacement of individual plumes more than the annual distribution of the emissions; we have not tested this explanation separately. The 10 m wind may still underestimate transport aloft, and Sect. 4.3 keeps this statement.
Comment 5
The architecture comparison is useful, but the differences among UNet-CBAM, spectral-fusion UNet, UNet-SA, and FNO are relatively small. The authors should avoid overemphasizing the superiority of one architecture and instead emphasize the robustness of the physics-constrained framework across different encoder backbones.
We agree with this reading. Sect. 3.1 now presents the comparison as evidence that the reconstruction skill depends little on the encoder: the four backbones reach r = 0.821 to 0.884, against 0.331 for EDGAR (0.795 to 0.859, against 0.332, on the 54 validation days, which were also used to select the checkpoint). In the revised comparison the spectral-fusion UNet scores slightly higher than UNet-CBAM (0.884 against 0.871). We kept UNet-CBAM as the production backbone because this difference is not resolved by the data: UNet-CBAM itself reaches 0.871 to 0.886 across four network initialisations. The emission patterns agree as well. The annual patterns obtained with the spectral-fusion UNet and with UNet-SA differ from the UNet-CBAM pattern by 1.3 and 1.4 % of the emissions at 0.5°, which is no more than the four UNet-CBAM initialisations differ from one another (0.7 to 1.5 %), so the conclusions do not depend on the choice. The comparison concerns reconstruction skill only, and we do not claim that one encoder gives more accurate emissions.
Comment 6
The authors are strongly recommended to cite recent work on high-spatiotemporal-resolution urban air-pollution monitoring. In particular, Yeganeh, B., Shakerdonyavi, A., Zafarmomen, N., and Taheri, A.: Comprehensive spatiotemporal analysis of long-term mobile monitoring for traffic-related particles in a complex urban environment, Atmospheric Pollution Research, 102870, 2025, is highly relevant. Although that study focuses on PM2.5 and black carbon rather than NOx emissions, it demonstrates the importance of dense, high-resolution observations for characterizing urban traffic-related pollution. Citing this work would strengthen the manuscript's motivation regarding the need for high-resolution emission and pollution fields beyond static inventories and fixed monitoring networks.
We thank the commenter for the suggestion and read the study with interest; long-term mobile monitoring is a valuable way to resolve urban gradients of traffic-related particles. Our manuscript addresses a different question: the satellite-based inversion of NOx emissions on a regional 0.1° grid, motivated by the uncertainty in where inventories place these emissions. Because the suggested paper concerns other pollutants, a different measurement approach and the urban street scale, we feel it would not fit the motivation of this manuscript, and we have not added it to the reference list.
Comment 7
Several figures are visually dense, especially Figures 2, 5, 10, 11, and 12. The authors should improve figure readability by increasing font sizes, simplifying legends, and ensuring that color scales and correlation annotations are easy to interpret.
Thank you. All figures have been redrawn. The schematic (Fig. 2) has been simplified and relabelled. Fig. 5 shows the three example days on one common colour scale, with each field divided by its geometric mean, and the correlation printed in each simulated panel. The submitted Figs. 10 to 12 have been replaced by figures on the annual redistribution (Fig. 8), its uncertainty (Fig. 9), the comparison with MEIC (Figs. 10 and 12) and the monthly fields (Fig. 11). Each caption describes the panels and states the colour scale, including the share of values outside the scale where it is not zero.
Citation: https://doi.org/10.5194/egusphere-2026-3233-AC1
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AC1: 'Reply on CC1', Yinan Wang, 27 Oct 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 -
AC2: 'Reply on RC1', Yinan Wang, 27 Oct 2026
We thank Referee #1 for the careful and constructive report. Our point-by-point response is provided in the attached supplement. Referee comments are given in blue and our replies in black. Text quoted from the revised manuscript is given in red, with its location. In brief, the revision addresses the referee's main points as follows. We now state that the TROPOMI columns constrain the spatial pattern of the emissions, not the domain total. We explain why EDGAR was chosen for the normalisation, and we report the effect of using MEIC instead. The redistribution metric is now defined explicitly. Its size is compared with a synthetic test with known emissions, which shows that a change of this magnitude also arises from the method itself. We discuss the low-prior grid cells in terms of how much information a single overpass carries there. Wording that described the evaluations as independent has been revised, and the figure with the inconsistent caption has been replaced. During the revision we also found that the TROPOMI quality screening stated in the manuscript had not been applied correctly when the columns were gridded. All data were re-gridded with the stated screening, all networks were retrained and all values were recomputed. Most numbers therefore differ from the discussion paper. The supplement lists the main changes.
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AC2: 'Reply on RC1', Yinan Wang, 27 Oct 2026
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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 -
AC3: 'Reply on RC2', Yinan Wang, 27 Oct 2026
We thank Referee #2 for the thorough and constructive report. Our point-by-point response is provided in the attached supplement. Referee comments are given in blue and our replies in black. Text quoted from the revised manuscript is given in red, with its location. We agree with the main point of the report: reconstructing the columns that the encoder receives is not evidence that the emissions are correct. The revised manuscript keeps the two apart. Agreement with the training decoder is now described as consistency with a design constraint. Tests with data that do not enter the inversion are reported separately, and a synthetic test with known emissions has been added. The decoder is described as a simplified transport and decay model, together with what it does not represent. "Daily" has been removed from the title, and the daily fields are described as effective emissions at the TROPOMI overpass time, not 24 h mean emission rates. The WRF-Chem configuration of all runs is given in a new table in the Supplement. The 12 to 15 % uncertainty has been replaced by a budget in which each source is estimated separately and the sources are combined. During the revision we also found that the TROPOMI quality screening stated in the manuscript had not been applied correctly when the columns were gridded. All data were re-gridded with the stated screening, all networks were retrained and all values were recomputed. Most numbers therefore differ from the discussion paper. The supplement lists the main changes.
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AC3: 'Reply on RC2', Yinan Wang, 27 Oct 2026
Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2026-3233', Nima Zafarmomen, 05 Jul 2026
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.
- The manuscript should more clearly distinguish between internal physical self-consistency and fully independent validation. Much of the reported improvement is based on the same differentiable decoder used during training, while the WRF-Chem test still uses TROPOMI NO₂ as the comparison reference. The authors should clarify the degree of independence of each validation step.
- The treatment of absolute emission magnitude needs further explanation. Since the rendering loss is demeaned and the annual total is normalized to EDGAR, the observations mainly constrain spatial patterns and temporal variability rather than absolute emissions. This limitation should be emphasized more clearly in the abstract, results, and conclusion.
- The chemical lifetime parameterization is central to the inversion framework. Although the authors provide sensitivity tests, the use of monthly scalar lifetimes may oversimplify spatial variability in photochemistry, boundary-layer conditions, and NOx chemical regimes. A more explicit discussion of how this assumption affects regional emission estimates would strengthen the manuscript.
- The use of ERA5 10 m winds to approximate column transport should be better justified. Since NO₂ columns reflect transport through the boundary layer and lower troposphere, the authors should discuss the potential implications of using near-surface winds rather than vertically resolved or PBL-weighted winds.
- The architecture comparison is useful, but the differences among UNet-CBAM, spectral-fusion UNet, UNet-SA, and FNO are relatively small. The authors should avoid overemphasizing the superiority of one architecture and instead emphasize the robustness of the physics-constrained framework across different encoder backbones.
- The authors are strongly recommended to cite recent work on high-spatiotemporal-resolution urban air-pollution monitoring. In particular, Yeganeh, B., Shakerdonyavi, A., Zafarmomen, N., and Taheri, A.: Comprehensive spatiotemporal analysis of long-term mobile monitoring for traffic-related particles in a complex urban environment, Atmospheric Pollution Research, 102870, 2025, is highly relevant. Although that study focuses on PM2.5 and black carbon rather than NOx emissions, it demonstrates the importance of dense, high-resolution observations for characterizing urban traffic-related pollution. Citing this work would strengthen the manuscript’s motivation regarding the need for high-resolution emission and pollution fields beyond static inventories and fixed monitoring networks.
- Several figures are visually dense, especially Figures 2, 5, 10, 11, and 12. The authors should improve figure readability by increasing font sizes, simplifying legends, and ensuring that color scales and correlation annotations are easy to interpret.
Citation: https://doi.org/10.5194/egusphere-2026-3233-CC1 -
AC1: 'Reply on CC1', Yinan Wang, 27 Oct 2026
We thank N. Zafarmomen for the interest in our work and for a constructive comment. Several of the points concern what the satellite columns can and cannot determine in this framework, and we have tried to answer them by explaining the reasoning behind the design and the tests that support it.
General comment
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.
Thank you for the summary. Two aspects of it deserve a clarification, because they bear on how the results should be read.
First, the quantity that the satellite constrains is the spatial pattern of the emissions, not their daily amount. The training loss compares simulated and observed columns after removing the domain mean of their logarithms, so any change of the domain-wide emission level leaves the loss unchanged. The revised title therefore speaks of "emission spatial patterns", and the products are annual and monthly patterns. The daily fields are effective emissions at the overpass time (about 13:30 local time); a single overpass does not determine a 24 h mean emission rate.
Second, a reduction of the domain-mean column bias in WRF-Chem is not evidence for the inversion. The domain total of PINE-NOx is fixed by the normalization to EDGAR, so a change of the mean bias reflects that design choice and the configuration of the chemical model rather than information from the satellite. In the revised WRF-Chem experiment all runs have the same NOx total inside the domain and differ only in the spatial pattern of the emissions, and the comparison is made on the pattern of the simulated columns and of surface NO2 (Sect. 3.2).
Comment 1
The manuscript should more clearly distinguish between internal physical self-consistency and fully independent validation. Much of the reported improvement is based on the same differentiable decoder used during training, while the WRF-Chem test still uses TROPOMI NO₂ as the comparison reference. The authors should clarify the degree of independence of each validation step.
We agree, and the revised manuscript states the independence of each test where it is reported. The table summarizes the four kinds of evidence.
Test
Shares with the inversion
What it can show
Reconstruction of the TROPOMI columns (Sect. 3.1)
the decoder and the observations
internal consistency; not a validation of the emissions
WRF-Chem columns against TROPOMI (Sect. 3.2)
the observations only
consistency with the fitted observations in an independent transport and chemistry model
WRF-Chem surface NO2 against 160 CNEMC stations (Sect. 3.2)
nothing
an independent test; in July 2023 it does not show the PINE-NOx pattern to be better than EDGAR
MEIC 2023 inventory (Sect. 3.3)
nothing
consistency with an independent bottom-up estimate; the PINE-NOx pattern is closer to MEIC than EDGAR is, clearly in July and not in January once a synthetic test with known emissions is taken into account (Sect. 3.3)
None of these tests is a complete validation of the emissions. The station comparison is the only observational test independent of the satellite, and its result is reported as it is; compared directly with the emissions in the station cells, the station NO2 also correlates slightly better with EDGAR than with PINE-NOx (log-space r = 0.365 against 0.306; Sect. 3.2, Fig. S6). An inventory comparison is informative but cannot decide which allocation is right, since MEIC has its own errors. Facility-level or flux observations would be needed for that, and the manuscript says so in Sect. 4.3. A synthetic test with known emissions, added in the revision, also shows that the method by itself produces a change of the pattern relative to EDGAR of about the size retrieved from the observations, so its size is no longer reported as an observed redistribution (Sect. 3.3).
Comment 2
The treatment of absolute emission magnitude needs further explanation. Since the rendering loss is demeaned and the annual total is normalized to EDGAR, the observations mainly constrain spatial patterns and temporal variability rather than absolute emissions. This limitation should be emphasized more clearly in the abstract, results, and conclusion.
We agree that the absolute magnitude is not constrained, and the abstract, Sect. 2.4, Sect. 2.5, Sect. 4.3 and the Conclusions now state this. One part of the comment needs a correction: the observations do not constrain the temporal variability of the domain-wide emissions either. Multiplying all emissions of a given day by a constant shifts the logarithm of the simulated column by a constant, which the demeaned loss removes. The same argument applies to every day separately, so neither the annual level nor its day-to-day or month-to-month variation is seen by the loss. What the satellite does constrain is how the emissions of a day are distributed in space, and averaged over the year, how the distribution differs from EDGAR.
For this reason the revised paper reports no domain-level variability. The monthly totals of the product follow the EDGAR monthly profile, so that the annual and monthly totals come from one inventory, and the domain annual total can be rescaled to another inventory (for example MEIC, 0.88 of the EDGAR total) without changing any pattern, share or correlation in the paper.
Comment 3
The chemical lifetime parameterization is central to the inversion framework. Although the authors provide sensitivity tests, the use of monthly scalar lifetimes may oversimplify spatial variability in photochemistry, boundary-layer conditions, and NOx chemical regimes. A more explicit discussion of how this assumption affects regional emission estimates would strengthen the manuscript.
The point is well taken, and it helps to separate two ways in which the lifetime enters. Under near steady state the column scales roughly with the product of emission and lifetime. A lifetime error that is uniform over the domain therefore changes all columns by approximately a common factor, which the demeaned loss removes (it also changes the length of the plumes, a smaller effect that the tests below include); it affects the regional level and the seasonal amplitude of the emissions, which the inversion does not report, but not their spatial pattern. Only spatial differences in the lifetime can be mistaken for spatial differences in the emissions.
We tested both by retraining the model with eight variants of the lifetime table (scaled by 0.7 and 1.3, without its seasonal cycle, with the winter months scaled by 0.67 and 1.5, with a seasonal shape following the O(1D) photolysis frequency with and without its latitude dependence, and with a spatial lifetime pattern diagnosed from a WRF-Chem simulation with full chemistry; Sect. 4.1). Across these variants the annual emission shares change by 1.4 % at 0.5° (1σ, emission-weighted), and the share of the 10 % highest-emitting cells changes by at most 2 percentage points, small compared with the difference of about 23 percentage points between PINE-NOx and EDGAR (58.6 % against 35.2 %), although a synthetic test with known emissions (Sect. 3.3) shows that a difference of that size also arises from the method itself. This term is part of the uncertainty budget (Fig. 9).
The seasonal amplitude is a different matter. The winter-to-summer ratio of the emissions implied by the columns ranges from 1.1 to 1.8 when the winter lifetime is changed by ±25 % (Sect. 3.3 and Fig. S12), so it cannot be determined in this way and is not reported as a result. Nonlinear chemical regimes are not represented by a first-order decay, and Sect. 2.2 now lists this among the simplifications of the decoder.
Comment 4
The use of ERA5 10 m winds to approximate column transport should be better justified. Since NO₂ columns reflect transport through the boundary layer and lower troposphere, the authors should discuss the potential implications of using near-surface winds rather than vertically resolved or PBL-weighted winds.
We agree that the column is transported by winds through the boundary layer, which are usually stronger than the 10 m wind and may turn with height. To quantify the effect, we retrained the model with the ERA5 100 m wind and with the boundary-layer mean wind in place of the 10 m wind. Across the three wind levels the annual emission shares differ by about 1 % at 0.5° and 3 % at 0.1° (1σ, emission-weighted), one of the smaller terms of the uncertainty budget (Fig. 9, Sect. 4.3).
Transport itself does matter: switching advection off lowers the reconstruction correlation from 0.871 to 0.778 (Sect. 4.1). We think the sensitivity to the wind level is small mainly because the annual pattern averages over many days with different wind directions and speeds, so that a systematic difference in wind speed changes the displacement of individual plumes more than the annual distribution of the emissions; we have not tested this explanation separately. The 10 m wind may still underestimate transport aloft, and Sect. 4.3 keeps this statement.
Comment 5
The architecture comparison is useful, but the differences among UNet-CBAM, spectral-fusion UNet, UNet-SA, and FNO are relatively small. The authors should avoid overemphasizing the superiority of one architecture and instead emphasize the robustness of the physics-constrained framework across different encoder backbones.
We agree with this reading. Sect. 3.1 now presents the comparison as evidence that the reconstruction skill depends little on the encoder: the four backbones reach r = 0.821 to 0.884, against 0.331 for EDGAR (0.795 to 0.859, against 0.332, on the 54 validation days, which were also used to select the checkpoint). In the revised comparison the spectral-fusion UNet scores slightly higher than UNet-CBAM (0.884 against 0.871). We kept UNet-CBAM as the production backbone because this difference is not resolved by the data: UNet-CBAM itself reaches 0.871 to 0.886 across four network initialisations. The emission patterns agree as well. The annual patterns obtained with the spectral-fusion UNet and with UNet-SA differ from the UNet-CBAM pattern by 1.3 and 1.4 % of the emissions at 0.5°, which is no more than the four UNet-CBAM initialisations differ from one another (0.7 to 1.5 %), so the conclusions do not depend on the choice. The comparison concerns reconstruction skill only, and we do not claim that one encoder gives more accurate emissions.
Comment 6
The authors are strongly recommended to cite recent work on high-spatiotemporal-resolution urban air-pollution monitoring. In particular, Yeganeh, B., Shakerdonyavi, A., Zafarmomen, N., and Taheri, A.: Comprehensive spatiotemporal analysis of long-term mobile monitoring for traffic-related particles in a complex urban environment, Atmospheric Pollution Research, 102870, 2025, is highly relevant. Although that study focuses on PM2.5 and black carbon rather than NOx emissions, it demonstrates the importance of dense, high-resolution observations for characterizing urban traffic-related pollution. Citing this work would strengthen the manuscript's motivation regarding the need for high-resolution emission and pollution fields beyond static inventories and fixed monitoring networks.
We thank the commenter for the suggestion and read the study with interest; long-term mobile monitoring is a valuable way to resolve urban gradients of traffic-related particles. Our manuscript addresses a different question: the satellite-based inversion of NOx emissions on a regional 0.1° grid, motivated by the uncertainty in where inventories place these emissions. Because the suggested paper concerns other pollutants, a different measurement approach and the urban street scale, we feel it would not fit the motivation of this manuscript, and we have not added it to the reference list.
Comment 7
Several figures are visually dense, especially Figures 2, 5, 10, 11, and 12. The authors should improve figure readability by increasing font sizes, simplifying legends, and ensuring that color scales and correlation annotations are easy to interpret.
Thank you. All figures have been redrawn. The schematic (Fig. 2) has been simplified and relabelled. Fig. 5 shows the three example days on one common colour scale, with each field divided by its geometric mean, and the correlation printed in each simulated panel. The submitted Figs. 10 to 12 have been replaced by figures on the annual redistribution (Fig. 8), its uncertainty (Fig. 9), the comparison with MEIC (Figs. 10 and 12) and the monthly fields (Fig. 11). Each caption describes the panels and states the colour scale, including the share of values outside the scale where it is not zero.
Citation: https://doi.org/10.5194/egusphere-2026-3233-AC1
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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 -
AC2: 'Reply on RC1', Yinan Wang, 27 Oct 2026
We thank Referee #1 for the careful and constructive report. Our point-by-point response is provided in the attached supplement. Referee comments are given in blue and our replies in black. Text quoted from the revised manuscript is given in red, with its location. In brief, the revision addresses the referee's main points as follows. We now state that the TROPOMI columns constrain the spatial pattern of the emissions, not the domain total. We explain why EDGAR was chosen for the normalisation, and we report the effect of using MEIC instead. The redistribution metric is now defined explicitly. Its size is compared with a synthetic test with known emissions, which shows that a change of this magnitude also arises from the method itself. We discuss the low-prior grid cells in terms of how much information a single overpass carries there. Wording that described the evaluations as independent has been revised, and the figure with the inconsistent caption has been replaced. During the revision we also found that the TROPOMI quality screening stated in the manuscript had not been applied correctly when the columns were gridded. All data were re-gridded with the stated screening, all networks were retrained and all values were recomputed. Most numbers therefore differ from the discussion paper. The supplement lists the main changes.
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AC2: 'Reply on RC1', Yinan Wang, 27 Oct 2026
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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 -
AC3: 'Reply on RC2', Yinan Wang, 27 Oct 2026
We thank Referee #2 for the thorough and constructive report. Our point-by-point response is provided in the attached supplement. Referee comments are given in blue and our replies in black. Text quoted from the revised manuscript is given in red, with its location. We agree with the main point of the report: reconstructing the columns that the encoder receives is not evidence that the emissions are correct. The revised manuscript keeps the two apart. Agreement with the training decoder is now described as consistency with a design constraint. Tests with data that do not enter the inversion are reported separately, and a synthetic test with known emissions has been added. The decoder is described as a simplified transport and decay model, together with what it does not represent. "Daily" has been removed from the title, and the daily fields are described as effective emissions at the TROPOMI overpass time, not 24 h mean emission rates. The WRF-Chem configuration of all runs is given in a new table in the Supplement. The 12 to 15 % uncertainty has been replaced by a budget in which each source is estimated separately and the sources are combined. During the revision we also found that the TROPOMI quality screening stated in the manuscript had not been applied correctly when the columns were gridded. All data were re-gridded with the stated screening, all networks were retrained and all values were recomputed. Most numbers therefore differ from the discussion paper. The supplement lists the main changes.
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AC3: 'Reply on RC2', Yinan Wang, 27 Oct 2026
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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.