the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Jul 2026
3+1D Spatiotemporal NO2 Mapping in Munich using DOAS Tomography and Bayesian Inference Methods
Abstract. We present, to the authors' knowledge, the first application of Bayesian inference to atmospheric differential optical absorption spectroscopy (DOAS) tomography resulting in a full 3+1D reconstruction of the NO2 concentration distribution from a long-path (LP) DOAS setup with 22 intersecting measurement paths. Four novel long-path DOAS instruments (HyDOAS) were deployed at the Ludwig-Maximilians-University main campus in Munich, complemented by point measurements from the Air Quality Inspection Box (AIRQUIX) sensor. Reconstructions were performed using the Numerical Information Field Theory for Python (NIFTy) inference framework with a combination of Metric Gaussian Variational Inference (MGVI) and geometric Variational Inference (geoVI), which provide access to the full posterior probability distribution. The reconstruction achieves strong internal consistency (overall reduced chi-squared = 0.518, Pearson correlation > 0.9), and remains consistent with independent point-sensor validation even under a more challenging low-concentration, high-wind scenario (reconstruction referenced chi-squared = 0.842). The method captures small-scale spatial features invisible to conventional point monitoring networks. Key findings reveal that under low-wind conditions, nitrogen dioxide (NO2) accumulates in building corners and low-ventilation zones, often tens of meters from emission sources, likely due to transport of nitric oxide (NO) from street emitters followed by oxidation and trapping in recirculation zones. Cross-validation against independent point sensor measurements demonstrates agreement within the posterior uncertainty prediction despite challenging low-concentration conditions. These results highlight the value of Bayesian tomographic reconstructions for exposure assessment and suggest that regulatory monitoring networks may not be fully representative for reflecting the actual pollution exposure of the population.
Competing interests: Stefan Schmitt is an employee of Airyx GmbH, which manufactures the HyDOAS instruments used in this study. The remaining authors declare no competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 01 Oct 2026)
- RC2: 'Comment on egusphere-2026-3941', Anonymous Referee #1, 21 Sep 2026 reply
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RC3: 'Comment on egusphere-2026-3941', Anonymous Referee #2, 21 Sep 2026
reply
The manuscript presents a Bayesian tomography field inference method to reconstruct the 3+1D spatiotemporal distribution of atmospheric NO2 concentrations in Munich. The experimental setup in Munich combines observations from four scanning long-path "HyDOAS" prototypes across 22 light paths with electrochemical in-situ measurements from an AIRQUIX low-cost sensor on the LMU Munich campus. Reconstructions are presented for two short time windows from a March–April 2025 campaign: 90 minutes on 15 April and 60 minutes on 23 April, the latter incorporating the AIRQUIX point sensor for data fusion.
Internal data consistency on 15 April is good (chi_red^2 = 0.518 and weighted correlations r_w > 0.86), whereas the 23 April reconstruction shows degraded DOAS–field agreement when the point measurement is included (HyDOAS 4 chi_red^2 = 2.375) and only moderate agreement between the DOAS-only field and the point sensor (r_w = 0.526; chi_rec-ref^2 = 0.842). The authors interpret low-wind reconstructions as evidence that NO2 accumulates in building corners and poorly ventilated zones tens of meters from street sources, arguing that conventional regulatory monitoring networks lack spatial representativeness in complex urban geometries. While the optical hardware deployment and 3+1D extension are technically ambitious, the manuscript has four major issues:
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Repetition of the authors' previous submission also to AMT (Henning et al., 2026, egusphere-2026-2724).
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An exceptionally small measurement sample (2.5 hours out of a two-month campaign).
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Information content in the spatial (3D) domain is over-interpreted to what the measurements actually constrains.
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Physical claims regarding building-corner accumulation are contradicted by the presented mean fields and confounded by posterior uncertainty (sigma/mu ≈ 0.7–0.8) and edge artifacts.
The urban 3+1D multi-instrument HyDOAS network deployment represents a valuable experimental contribution, but the manuscript in its current form overstates its methodological novelty similar to Henning et al. (2026, egusphere-2026-2724), bases major conclusions only on ~2.5 hours of selected data with low concentrations (near instrument detection limits), and the "corner accumulation" claim is inconsistent with high-uncertainty path-edges. The authors must expand the sample size to show how the method works in various conditions, and separate new developments from their previous work.
Major Comments
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The core inference method in Section 3.3 (Eqs. 2–8), applying NIFTy, MGVI, geoVI, softplus positivity, line-of-sight response operators, and separable Gaussian random field priors to LP-DOAS and point sensor data, was previously presented in Henning et al. (2026) (egusphere-2026-2724).
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The primary evolution is the domain dimensionality and science target: extending from 2+1D intermediate fields for vertical profiling (CINDI) to a 3+1D urban courtyard tomography grid. While scaling to 3+1D is a substantial experimental and computational step, it represents an application scaling rather than a fundamental mathematical advance.
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The claim that this work is "to the authors' knowledge, the first application of Bayesian inference to atmospheric DOAS tomography" resulting in "full 3+1D" is overly broad.
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Despite a field campaign running from ~01 March to 23 April 2025, the manuscript presents an evaluation of only 2.5 hours of data (90 min on 15 April; 60 min on 23 April). Evaluating two brief, isolated time windows provides insufficient cases to assess the stability, robustness, or operational utility of the reconstruction scheme.
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Validation with the single AIRQUIX in-situ sensor for only 60 minutes under high-wind (4–6 m/s) conditions where NO2 mixing ratios dropped below 5 ppb, which is at or near the detection limits of the HyDOAS and AIRQUIX instruments. Even under the low concentration condition, the correlation with AIRQUIX is not good, yielding a high cost function when fusing AIRQUIX observations into the scheme.
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Given the mobility and low cost of the AIRQUIX unit, I cannot understand why the authors only deploy a single unit at one fixed location for one hour. Deploying multiple sensors across building corners, shadow zones, and path intersections would have provided the ground truth required to validate the tomographic scheme.
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The Abstract and Section 5.3 state that NO2 systematically "accumulates in building corners and low-ventilation zones, often tens of meters from emission sources". However, I cannot see that in Figure 9.
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The transport mechanisms proposed in Section 5.1.1 (NO emission, oxidation to NO2, and vortex/recirculation trapping near building corners and trees) are speculative. Without wind vector fields, micro-scale turbulence data, or Microscale Meteorological Models (CFD), these mechanisms remain unverified.
Technical Comments
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The claim regarding "the first application of Bayesian inference to atmospheric DOAS tomography" is not true, as it has already been implemented in the authors' previous publication (Henning et al., 2026).
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Electrochemical sensors suffer from cross-sensitivities to O3, relative humidity, and thermal drift. Detail how environmental corrections and zero-point drift checks were performed for the 23 April deployment in the sub-5 ppb regime.
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High weighted correlation coefficients (r_w > 0.86) in Table 2 demonstrate that the model reproduces line integrals used in the fit; they do not validate unobserved voxels (building corners, shadow zones). Distinguish "data misfit" from "field reconstruction accuracy."
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In Table 3 (AIRQUIX included), HyDOAS 4 exhibits a high chi_red^2 = 2.375 and R_w^2 = 0.310, whereas in Table 4 (DOAS-only), it improves to chi_red^2 = 1.156 and R_w^2 = 0.671. This performance drop indicates spatial representativeness mismatches or systematic calibration offsets between optical paths and the point sensor.
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Prior assumptions (Initial Offset = 5, Log-slope, Length scales) strongly influence unconstrained domain corners. Provide sensitivity analyses showing how reconstruction features vary when spatial correlation length scales are modified.
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Section 5.2 notes that fixed temporal priors are suboptimal under high-wind conditions. Evaluate whether day-specific temporal correlation lengths or wind-informed anisotropic priors improve reconstruction fidelity.
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Eight 2 m vertical layers with limited vertical path diversity constrain true 3D resolving power. Provide a vertical path-density plot to justify the vertical layer choices.
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Wind parameters are taken from a campus weather station. Clarify its distance and elevation relative to the courtyard, as urban canyon micro-breezes often diverge from rooftop meteorological measurements.
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Clarify explicitly how optical path integrals near or below the ~5 ppb instrument detection limit are handled in the Gaussian log-likelihood formulation.
Citation: https://doi.org/10.5194/egusphere-2026-3941-RC3 -
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Henning et al. present (a) a tomographic method to derive the spatiotemporal distribution of NO2 based on Bayesian Inference and (b) application of this method to measurements in Munich.
(a) The Bayesian Inference Method reads interesting and innovative, but it has been already published by the same first author in a different study:
https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2724/
Section 3.3.1 is quite similar to the respective section in the previous paper, giving the same equations, while no reference to the previous paper is provided here.
(b) The measurement setup in Munich looks very interesting and promising on first sight: multiple LP-DOAS instruments and light path in a confined area around a major road in central Munich. But in sharp contrast to the costly setup of the LP instruments and retro-reflectors, very few measurements are actually available. Only for two days measurements are presented in this study. Most of all, the in-situ measurements from AIRQUIX have only been performed on one single day, and this particular day turned out to have suboptimal meteorological conditions. As the AIRQUIX is low-cost and portable, I do not understand why not several sensors have been installed, or the one available sensor has been operated on multiple days at different locations. This would have helped a lot for evaluating the actual performance of the proposed inversion scheme. In particular it would have allowed to test the key conclusion of the paper that NOx accumulates in building corners.
This key finding I find anyhow hardly supported by the data: In Fig. 9, highest concentrations are found in the center, while the corners on the left show medium values, and the corner at the right shows the absolute minimum.
With the presented measurements, it is unclear to me if the derived spatial distribution in particular in the corners reflect real variations in NO2 distribution or rather edge effects of the tomographic approach.
Thus, the submitted paper does neither provide a new method (see https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2724/) nor convincing results, and the claims of the study ("The method captures small-scale spatial features"; "NO2 accumulates in building corners") are not supported by the measurements.
Thus I cannot recommend publication in AMT.