Feasibility and Optimization Analysis of Discrete-Wavelength DOAS for NO₂ Retrieval Based on TROPOMI and EMI-II Observations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

General comments

This manuscript introduces and describes a modified Differential Optical Absorption Spectroscopy (DOAS) method called Discrete Wavelength DOAS (DWDOAS), designed to retrieve nitrogen dioxide (NO₂) vertical column densities (VCDs) using only a sparse set of 14 discrete wavelengths instead of full hyperspectral data. The primary motivation is to support the development of lightweight, efficient spectrometers for satellite remote sensing, which could reduce data volume, computational demands, and enable faster imaging without mechanical scanning. The study leverages Level 1B radiance data from two satellite instruments: TROPOMI on Sentinel-5P (European Space Agency, launched 2017) and EMI-II on GaoFen-5B (Chinese Academy of Sciences, operational since about 2022). Key contributions include wavelength optimization via an entropy-weight method (EWM), simulation of varying spectral resolutions (FWHM from 0.5 to 3.0 nm), and performance comparisons against traditional DOAS, focusing on error distributions, uncertainty, and detection limits.

The introduction provides a solid background on NO₂'s atmospheric role, sources, and health impacts, citing WHO and prior studies effectively. It contrasts in-situ methods (e.g., chemiluminescence) with remote sensing (e.g., MAX-DOAS, satellites), highlighting DWDOAS as a bridge to discrete-channel approaches like TOMS observations or SO₂ cameras. The methods section details spectral retrieval via Lambert-Beer law, SVD for inversion stability, Gaussian convolution for resolution simulation, and metrics like Information Retention Ratio (IRR), Noise Suppression Index (NSI), and a composite Score. The Results section analyzes retrievals from specific satellite orbits (TROPOMI: Dec 20, 2020; EMI-II Dec 10, 2024), showing correlations >0.98 in polluted areas but higher uncertainties in clean/low-latitude regions. The conclusion summarizes feasibility while noting limitations and future outlooks.

The paper is well written and logically structured: Introduction, Retrieval Method, Data and Setup, Results, Conclusions. It includes 9 figures and 5 tables very useful to follow and understand the manuscript.

Noteworthy points

The DWDOAS method innovates by combining DOAS's physical consistency with discrete-wavelength efficiency, reducing spectral dependency while maintaining retrievals. The EWM for optimizing wavelength-resolution pairs is a novel, objective approach, assigning weights based on entropy, avoiding subjective tuning. Simulations across 11 FWHM values reveal an optimal ~2.0 nm resolution, balancing signal fidelity (high IRR at low FWHM) and noise suppression (low NSI at high FWHM), as quantified by the Score metric. This is supported by robust math: SVD pseudoinverse for ill-conditioned matrices, Gaussian ISF for convolution, and Limit Of Detection as 3σ.

Using real L1B data from two complementary instruments (TROPOMI: higher resolution 0.45-0.65 nm, EMI-II 0.3-0.5 nm) improve the strength of the method. Orbit-specific analyses (e.g., Pacific clean regions for background noise) show spatial error patterns: clustered in low-latitudes due to aerosols/clouds, uniform in high-latitudes. Correlations and Gaussian-fitted error distributions demonstrate consistency. Monte Carlo simulations confirm random errors dominate, with lower confidence intervals. Per-pixel uncertainty/LOD comparisons highlight DWDOAS's higher variability ((0.4-1.2)×10¹⁵ vs. DOAS's (0.2-0.6)×10¹⁵ for TROPOMI), providing honest limitations.

The paper effectively addresses spectrometer design trade-offs: sparse sampling enables 2D spatial imaging on detectors, reducing scan times for dynamic processes. It notes DWDOAS's suitability for high-NO₂ areas and suggests applications to other gases like HCHO.

Suggestions to improve the paper

Include AMF sensitivity; test non-Gaussian ISFs; add multi-orbit/seasonal validations.

Cross-validate with ground networks (Pandonia Global Network for NO₂ VCD, NDAAC/ACTRIS Reactive trace Gases Remote sensing). Analyze error sources via covariance matrices

Expand conclusions with quantified benefits (e.g., data reduction %); add section on assumptions/limitations.

Specific comments

Line 77 – Non-contact…do you mean remote sensing?

Line 82 – ‘fusion’, please replace with ‘synergies’

Line 200 – [Error….], Please remove or update the reference field

Line 280 – ‘sampling interval of approximately 0.195 nm’, do you mean that each pixel of the sensor covers 0.195nm?. Please clarify?

Line 288-290 – Please clarify the data dimensions of the Visible-1 Channel. Moreover, it’s the information about the EMI-II FOV so important? In case of positive answer please provide the same also for TROPOMI.

Line 325 – ‘Score’ is an important parameter in this work, please highlight this putting in italic…

Table 4 and 5 – What is the superscript before w1? Please clarify.

Figure 9 – The color bar should have the same limits to have a uniform and more intelligible view of the Heatmap for the TROPOMI and EMI-II Index

Finally, this is a valuable, innovative contribution to atmospheric remote sensing, particularly for resource-constrained satellites. With strong methodology and real-data application, it merits publication in Remote Sensing after addressing the editorial flaws, and implementing the comments/suggestions above mentioned.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This study develops a Discrete Wavelength Differential Optical Absorption Spectroscopy (DWDOAS) method, using satellite observation data from TROPOMI and EMI-Ⅱ to retrieve the spatial distribution of atmospheric NO₂ column concentrations and comparing it with traditional DOAS methods. The authors use the entropy weight method to select wavelength-resolution combinations and attempt to simulate the effect of spectral random noise through Gaussian fitting and Monte Carlo simulations. The focus of the study is on reducing spectral sampling requirements, which is a significant issue for research in this field and important for simplifying calculations. However, the credibility of the data in the study is seriously problematic, and the authors need to clarify these issues carefully before the manuscript can be considered for publication.

major comments：

1. I believe the most serious issue in this study is that several key result figures (e.g., Figures 3 and 4) show significant contradictions in the data. First, there are numerous green and yellow pixels in Figure 3, and roughly estimating their proportion, they account for more than 30% of the entire track data, indicating that the error color scale in the figure is set too small. Secondly, the largest errors are observed at the central position of the entire track image (near the sub-satellite point), which contradicts the general precision distribution pattern for satellite products. Thirdly, with such large errors, the error probability density in Figure 4 follows a normal distribution, but in Figure 3, zero error is very rare. Therefore, the authors should provide a reasonable explanation for this serious contradiction.
2. The DWDOAS method is highly sensitive to wavelength selection and spectral configuration, yet the manuscript does not clearly specify the optimal wavelength combinations used by TROPOMI and EMI-Ⅱ, nor does it clearly explain the specific discrete wavelengths corresponding to the different combinations listed in Table 4. The wavelength combinations themselves are critical factors determining the algorithm's performance. The authors should provide necessary explanations and clarifications.
3. All performance evaluations in this study are based on internal comparisons with the "traditional DOAS implemented in this study," without a comparison with the widely accepted TROPOMI official NO₂ Level 2 products. Therefore, it is impossible to prove the actual value of the DWDOAS retrieval results in terms of absolute accuracy and practical applications. Additionally, the manuscript does not compare DWDOAS with existing discrete wavelength/low spectral information inversion methods. The authors should include a spatial distribution comparison of DWDOAS retrieval results with TROPOMI official products, scatter plots, and correlation analysis, and quantitatively compare the accuracy of DWDOAS with other similar algorithms reported in the literature to clarify the advantages and applicable scenarios of the proposed method.
4. The experimental design lacks sufficient time scale. This study evaluates the DWDOAS algorithm based solely on single-day observations, yet the authors emphasize the method's advantages in computational efficiency and large-scale applications. Without supporting inversion results over a longer time scale, the stability and robustness of the algorithm, as well as its actual advantages over traditional DOAS, cannot be fully verified. It is recommended to extend the experiment’s time scale (e.g., to several months or a year) and present convincing results from a longer time series.
5. The authors designed the algorithm to enhance inversion computational efficiency, and the manuscript repeatedly emphasizes that DWDOAS improves computational efficiency. However, there is a lack of quantitative data on the reduction in computation time or complexity (e.g., DWDOAS is X times faster than traditional DOAS when processing the same dataset). Furthermore, in the trade-off between precision and speed, the authors have not provided a clear quantitative relationship. For example, how much accuracy is lost at typical pollution concentrations? How much does the detection limit deteriorate in a clean background? Providing such data would allow readers to better judge the trade-off between speed improvement and accuracy loss. It is recommended that the results section includes statistics on how DWDOAS performs in terms of error, detection limits, and computation time across different concentration intervals (e.g., clean, moderate, and high pollution).

minor comments：

1. The results from different tracks in Figure 5 are suggested to be stitched together into a global-scale display to enhance spatial continuity and overall readability. Similarly, for Figure 7, it is recommended to use a global stitched result.
2. The results in Figure 7 appear almost entirely in a single blue color, making spatial differences hard to distinguish and not providing useful information. It is recommended that the authors reduce the upper limit of the color scale and adjust the display range to highlight regional differences.
3. The images in Appendix A have low resolution and lack necessary explanations, making it difficult for readers to understand the specific meaning of the 14 images presented. From the context, it is assumed that these images correspond to 14 candidate discrete wavelengths or wavelength combinations, but Table 4 only lists 10 combinations, and the relationship between them is unclear. The authors should clarify the physical meaning of the images in Appendix A and their correspondence to the wavelength combinations in the main text to avoid conceptual confusion.
4. Tables (e.g., Tables 4 and 5) do not uniformly mark the "optimal configuration" (e.g., with bold or annotations). It is recommended that the authors clarify the evaluation criteria for determining the optimal results in the table captions and highlight the best results to help readers quickly understand.
5. In some parts of the manuscript, there are unclear correspondences between result descriptions and figure numbers. For example, when citing figures, the specific subfigures (e.g., Fig. 3a, Fig. 3b) are not clearly indicated. It is recommended to label the subfigures clearly when multiple subfigures are involved to avoid ambiguity.
6. The figure captions are too brief in explaining the contents of the figures, and some figures require the main text for context. It is recommended to provide more detailed explanations in the figure captions about the variables, algorithm types (DWDOAS or DOAS), and statistical or computational methods to enhance the self-explanatory nature of the figures.
7. In some figures (e.g., Figures 3, 4, and 10), the font size, axis scale, and color bar labeling are not consistent. It is recommended that the font size, unit labels, and color bar formats for all figures be standardized to improve overall layout quality and professionalism.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript proposes a low-spectral-information retrieval strategy for rapid atmospheric monitoring to address the limitations of traditional nitrogen dioxide (NO2) retrieval methods, such as large data volume, low computational efficiency, and complex instrument requirements. The findings suggest that reliable NO2 retrieval performance can be maintained while substantially reducing spectral information demands, offering practical implications for the design of low-resolution spectrometers, onboard data compression, and wide-area, high-frequency trace-gas monitoring. However, I have several concerns that should be addressed to strengthen the manuscript:

 

(1) In line 200, there appears to be an issue with the citation format. Please carefully check and correct the reference style throughout the entire manuscript for consistency and accuracy.

(2) When discussing the results in Figure 3, the authors suggest that errors may be related to aerosol load, boundary layer structure, and algorithmic sensitivity to concentration gradients. To substantiate these claims, it is recommended that the authors provide and analyze supporting data or products (e.g., aerosol optical depth, boundary layer height) to corroborate the observed spatial error patterns.

(3) The accuracy of the traditional DOAS retrieval under low NO2 concentration conditions is crucial for a meaningful comparison with the proposed DWDOAS method. If the DOAS retrieval itself lacks reliability at low concentrations, any subsequent comparative analysis with DWDOAS would be questionable. The authors should clarify the validation of DOAS retrievals against reference measurements (e.g., ground-based observations) under such conditions, or discuss the known limitations and uncertainties of DOAS in low-concentration scenarios.

(4) The authors should provide a more detailed and concrete analysis of the potential applications and limitations of the DWDOAS method. In which specific scenarios or regions might it be most advantageous? Conversely, under what conditions might its performance degrade? A clearer discussion on the operational prospects, including possible constraints and recommended use cases, would help readers better assess the method's practical utility.

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

Recommendation: Major changes

Evaluation:

This study evaluates the feasibility and performance of a discrete-wavelength DOAS approach for satellite-based NO₂ retrieval. By reducing spectral information, the method aims to improve efficiency and lower data and instrumental requirements, and its performance and limitations are systematically assessed using TROPOMI and EMI-Ⅱ observations. Below are some suggestions for improvement:

 

Major comments

 

1. In Figure 10, the VCD uncertainty is shown with shaded intervals, whereas the LOD is presented without shading. It is recommended to provide a brief explanation of this design choice in the figure caption or accompanying text.
   2. Table 1 lists the main parameters of TROPOMI and EMI-II, but it does not explicitly reflect information directly relevant to the DWDOAS method within the target wavelength range (420–450 nm). It is recommended that specific performance indicators pertinent to this method be added.
   3. It is suggested that a technical workflow diagram be included in Section 2 of the manuscript to visually illustrate the complex methodological processes involved, such as spectral convolution, SVD-based retrieval, and entropy-weight optimization.
   4. The manuscript selects 14 representative wavelengths based on NO₂absorption features, but does not describe any sensitivity analysis or optimization for wavelength screening, nor discuss the impact of wavelength calibration errors. Clarification and brief discussion are recommended.
   5. The article claims to have proposed a new method, DWDOAS. However, from the perspective of mathematical modeling, its inversion framework does not essentially differ from the traditional DOAS. DWDOAS still relies on linear least squares fitting of absorption cross-sections with polynomial terms, without introducing new inversion theories, prior constraints, or regularization mechanisms. The distinction of "DWDOAS" in this paper mainly lies in the discrete wavelength sampling and reduced spectral resolution, rather than any innovation in the inversion model itself. The authors should clearly state whether DWDOAS is merely an implementation of DOAS under discrete wavelength conditions and adjust the descriptions of "novelty" throughout the text accordingly, to avoid misrepresenting engineering-level improvements as a new inversion method.
   6. The experimental design for the comparison between DWDOAS and traditional DOAS has a problem of confounding variables. In the section 3.2 of the article, which discusses the fitting parameter settings for NO2 retrieval, multiple key parameters change simultaneously when comparing DWDOAS with traditional DOAS, including the number of wavelengths, the order of the polynomial, and whether correction is performed. This non-single variable change setting makes it impossible to distinguish whether the performance difference is due to the discrete wavelength sampling itself or the change in wavelength correction strategy. The author should discuss this confounding issue or supplement experiments to illustrate the relative impact of different factors on the results; otherwise, the current explanation of the advantages of DWDOAS is not rigorous.
   7. Regarding the core innovation of the paper, the DWDOAS method enhances computational efficiency in NO₂inversion through discrete wavelength selection. While it provides only a qualitative analysis of this efficiency gain, it does sacrifice inversion accuracy to some extent. Is this a limitation of the method?

 

Minor issues

 

1. At line 200, the text “[Error! Reference source not found]” appears. Please verify and correct this reference error.
2. In Equation (13) at line 262, “NO2” is recommended to be revised to “NO₂”.
3. At line 300, the text states “...and their absorption cross-sections are shown in Figure 2.” However, according to the description, the corresponding figure is labeled as Figure 1 (line 312). Please verify and ensure consistency.
4. The conclusion states that DWDOAS is suitable for regions with high NO₂ concentrations, but the quantitative threshold defining “high concentration” is not specified. In addition, potential improvement strategies for clean regions are not discussed. It is recommended that the authors clarify the applicability threshold and propose possible directions for improvement.
5. In Figure 1, the subscripts of the gas species are incorrectly positioned. They should be placed at the lower right.
6. The scatter plots in the manuscript only present the correlation coefficient (R) and the fitted regression line. It is further recommended that the total sample size, RMSE, and other relevant statistical metrics be annotated in the figures.
7. Section 4.1 discusses data from December 20, 2022, whereas the caption of Figure 5 incorrectly states “December 20, 2020.” This discrepancy in dates should be corrected to ensure consistency between the text and the figure.

Comments for author File: Comments.pdf

Author Response

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Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have responded to all my questions one by one. However, I still suggest that a more reliable error result can be obtained by comparing with other official products, rather than just comparing the two methods used by oneself. I hope the author will consider this suggestion.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

I have no further comments. 

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The author has made revisions to the raised issues. In my opinion, the current version is acceptable.

Author Response

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