A New NO<sub>2</sub> Profile Retrieval from a Combination of Scanning Long-Path DOAS and Point Measurements Using Bayesian Inference-Based Spatiotemporal Reconstructions

Henning, Manuel; Haim, Philipp; Schmitt, Stefan; Lampel, Johannes; Pöhler, Denis; Wenig, Mark

doi:10.5194/egusphere-2026-2724

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https://doi.org/10.5194/egusphere-2026-2724

Preprints

16 Jun 2026

| 16 Jun 2026

A New NO₂ Profile Retrieval from a Combination of Scanning Long-Path DOAS and Point Measurements Using Bayesian Inference-Based Spatiotemporal Reconstructions

Manuel Henning, Philipp Haim, Stefan Schmitt, Johannes Lampel, Denis Pöhler, and Mark Wenig

Abstract. This study presents a fully Bayesian approach for retrieving reliable vertical profiles of nitrogen dioxide (NO₂) from a combination of path and in-situ measurements. Instead of focusing on complete two-dimensional reconstructions, we employ a three-dimensional correlated field model (2D in space + 1D in time) as a physically consistent intermediary step to extract profile information. The Bayesian inference framework, implemented using the Numerical Information Field Theory for Python library (NIFTy), allows for a rigorous propagation of measurement uncertainties and explicitly includes spatial and temporal correlations. Data from the CINDI-III campaign, including two in-situ ICAD devices and a new DOAS system, were used as input. The new DOAS system consists of a fast scanning active and passive DOAS instrument that can be used for Long-Path as well as MAX-DOAS measurements, called HyDOAS (Hybrid Differential Optical Absorption Spectroscopy). The resulting profiles were compared against independent MAX-DOAS retrievals as a consistency check. Our results demonstrate that the Bayesian spatiotemporal framework yields physically consistent and temporally coherent NO₂ profiles that agree well with established methods within their uncertainties. The approach offers a promising pathway to derive high-quality vertical information even from geometrically limited measurement configurations.

Received: 12 May 2026 – Discussion started: 16 Jun 2026

Competing interests: S.S., J.L., and D.P. are employees of Airyx GmbH, which manufactures the HyDOAS and ICAD 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.

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Manuel Henning, Philipp Haim, Stefan Schmitt, Johannes Lampel, Denis Pöhler, and Mark Wenig

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-2724', Anonymous Referee #1, 13 Jul 2026
General remarks
Henning et al. present a profile retrieval scheme based on Long-Path DOAS and in-situ measurements made during the CINDI-3 campaign at the Cabauw measurement tower. The paper matches the scope of AMT, and the method appears innovative and sound.

However, the benefit of this new profile retrieval remains limited, as the setup requires a high measurement tower. In addition, horizontal information is very limited, unless viewing geometry and location of in-situ measurements would be modified (which then would make the setup more complex and would probably require two towers / tall buildings).

The authors compared their results to MAX-DOAS profiles based on the M3 algorithm. Here, additional comparisons to other MAX-DOAS profile retrievals would be interesting.

I recommend publication on AMT after dealing with the issues listed below. In particular, the authors might consider how far the 2D retrieval is really providing added value, or directly use a 1D retrieval scheme instead. Further MAX-DOAS comparisons should be added.
(a) Partial profiles
Surface concentrations are measured by in-situ networks and are essential for air quality / health issues.

Tropospheric profiles are important for satellite validation (where AMFs require profile assumptions).

But what is the added value of partial profiles within the lower boundary layer? This should be motivated in more detail in the introduction.
The proposed retrieval scheme yields partial profiles of NO2 from ground to an altitude of ~200 m.

The upper limit is defined by the height of the highest retro-reflector, which is somehow trivial, but still an important information for the reader to be added in the instrument setup description. In addition, this should be also discussed in section 7, as this limits future applications of the proposed method to measurement sites next to tall towers or tall buildings (that allow for the installation of retro-reflectors), which are probably quite challenging to find.
(b) 2D retrieval
The authors present 2D (x, z)+1D (t) fields of NO2. However, in section 7, they point out that
"All light paths lie nearly in one vertical plane connecting the HyDOAS emitter and the KNMI tower, creating a largely symmetric setup."
causing
"the reconstructions to be more reliable in the vertical than in the horizontal direction."
The authors conclude that
"The observed smooth horizontal gradients in the posterior mean fields thus reflect prior-driven regularization rather than measurement-driven features."
With these conclusions, some earlier statements are not actually solid:
Line 36 ff:
This 2+1D formulation provides the physical consistency required to derive meaningful vertical

gradients and boundary-layer structure
Line 324 ff:
This anomaly suggests that significant horizontal variability in NO2 concentration occurred at that

time, challenging the underlying model assumptions and potentially leading to the overestimation in the upper layer. The 2D

reconstructions in Fig. 2 supports this hypothesis.
Please revise.
The information content on horizontal gradients is poor due to the measurement setup. In addition, there is no other data available which would allow for investigating the retrieved horizontal gradients, as both MAX-DOAS profile inversion and boxlayers assume horizontal homogeneity.

Thus, why should 2D fields be investigated at all? Instead, a 1D profile inversion could be set up directly, instead of starting with 2D and averaging horizontally later.
(c) MAX-DOAS comparison
The retrieved vertical profiles have been compared to profiles based on MAX-DOAS inversions with the M3 algorithm.

To my knowledge, within CINDI-3, vertical profiles are also routinely inverted by the FRM4DOAS processor, which uses two different algorithms, MMF and MAPA. Have the authors also compared their results to the FRM4DOAS products? This would provide additional information on the consistency of different MAX-DOAS inversion schemes.
The profile inversion from MAX-DOAS is in principle similar to the profile retrieval from the LP-DOAS measurements presented here.

In both cases, profile information is derived from a limited set of slant column measurements for different viewing geometries.

Thus, it would be interesting if the authors could comment on how far the Bayesian Inference-Based Spatiotemporal Reconstructions approach might also be used for MAX-DOAS profile retrievals.
(d) Sonde measurements
To my knowledge, there have been direct profile measurements with sondes performed during CINDI-3. Could these measurements be used for comparisons as well?
(e) Temporal coverage
The CINDI-3 campaign lasted several days. Please comment on the availability of profile retrievals for other days and add them to the appendix if available.
Detailed comments
Line 20: Please add references for LP-DOAS.

Line 23: Please add references for MAX-DOAS (original papers instead of text book).

Line 49: "we compare the NIFTy reconstructions with established methods such as MAX-DOAS profile retrievals." -> how far are compared methods "established"? Different MAX-DOAS profile inversion schemes can still result in considerably different vertical profiles.

Section 3: At first, the measurement site Cabauw with the feature of the KNMI tower and the CINDI-3 campaign should be introduced. The reference to the CINDI-3 presentation at EGU should be replaced or complemented by the CINDI-3 comparison paper to be submitted soon. Please replace "CINDI III" by "CINDI-3" throughout the manuscript.

Line 144 and throughout the paper: All dates should be given in ISO format (yyyy-mm-dd).

Text in subscript (e.g. Eq. 3) should be "textified", not variables (italic)

Fig. 2: axis labels and especially time stamps are hard to read. Please increase font size, and try a different (sans serif) font.

Fig. 4:
caption: "MAX-DOAS measurements" -> "vertical profiles inverted from MAX-DOAS measurements"

boxlayers: Why are there so many boxlayer values missing?

errors: Due to measurement geometry, I would assume a general increase of uncertainty with altitude, which could also be seen in Fig. 2. So why do the error range in Fig. 4 does not significantly increase with altitude?
Citation: https://doi.org/10.5194/egusphere-2026-2724-RC1
RC2:
'Comment on egusphere-2026-2724', Anonymous Referee #2, 21 Jul 2026
The manuscript presents an approach to atmospheric trace gas tomography by combining Scanning Long-Path Differential Optical Absorption Spectroscopy (LP-DOAS) with in-situ ICAD measurements to reconstruct vertical NO2 profiles. The authors used Numerical Information Field Theory (via the NIFTy framework) and frame the retrieval as a 2+1D continuous Bayesian problem.

The paper is mathematically sophisticated, and fits well with the scope of AMT. The use of full Bayesian inference to propagate non-Gaussian uncertainties across time and space is a new attempt to solve the problem over traditional regularized least-squares or static optimal estimation approaches.

However, there are issues that must be addressed before the manuscript can be accepted for publication. Primarily, the information content regarding the 2D spatial domain is definitely over-interpreted relative to what the sparse viewing geometry actually constrains, and the independent validation against CINDI-3 benchmark data needs to be substantially expanded.

Major Comments

The authors introduce the model as a "2+1D" spatial-temporal retrieval. However, they mentioned in Section 7, all light paths lie on a single vertical plane between the instrument and the Cabauw tower where retroreflectors were installed. The authors acknowledge that "The observed smooth horizontal gradients in the posterior mean fields thus reflect prior-driven regularization rather than measurement-driven features." If horizontal variability is governed by prior covariance functions rather than measurement, claiming a "2D reconstruction" is somehow misleading. Because this inversion setup is underdetermined, an infinite number of spatial concentration distributions could yield the exact same path-integrated measurements, and the reconstructed field is heavily dependent on the chosen prior hyperparameters and smoothing constraints. Furthermore, using these prior-driven horizontal gradients to explain upper-layer anomalies (e.g., lines 324) constitutes unproven speculation based on model artifacts. The manuscript must explicitly distinguish between measurement-constrained features and prior-driven artifacts. To address this, the authors should perform a rigorous prior sensitivity analysis demonstrating how varying both spatial and temporal correlation lengths impacts the retrieved profiles and uncertainty bounds.

The physical constraint of requiring a 200" m" tower for retro-reflector placement severely limits the operational portability of this vertical profiling setup, as tall infrastructure is exceptionally rare. A more common, scalable, and practical application of scanning LP-DOAS is horizontal tomography over urban, industrial, or complex terrain (where retro-reflectors can be placed on existing buildings). However, horizontal domains are typically dominated by localized emission hotspots, sharp traffic gradients, and industrial stack plumes. In such environments, the assumption of spatial smoothness enforced by the NIFTy priors could severely smooth out real, localized gradients or misallocate emissions across light paths. The manuscript currently lacks a clear motivation for sub-200" m" vertical profiling and fails to address how their inversion framework would translate to more practical horizontal geometries. The authors should explicitly discuss the portability and scalability of their framework. They should evaluate how their spatial smoothness assumptions would perform when applied to horizontal tomographic setups, where strong spatial gradients and localized emission hotspots undermine the assumption of spatial homogeneity.

Even within the rural setting of Cabauw, localized high-gradient events occur—such as agricultural machinery (e.g., tractor emissions), local surface inversion layers, or short-lived plumes. To prove that the Bayesian framework can handle sharp spatial and temporal dynamics without over-smoothing, the authors should evaluate how their spatial smoothness assumptions would perform when applied to high gradient fields. The authors should present a targeted case study featuring a localized, high-gradient event at Cabauw (e.g., a sharp transient plume detected by the in-situ ICAD instruments) to demonstrate whether the retrieval can resolve sharp structures or if the priors artificially dilute them into surrounding light paths.

To validate the retrieval, the authors compare their results solely against MAX-DOAS profiles derived from the M3 inversion algorithm. However, CINDI-3 was an intensive measurement campaign, and direct vertical profile observations (such as NO2 sondes) were conducted that are currently absent from the comparison. To ensure a comprehensive evaluation, the authors should include these direct in-situ profile measurements where available. The authors should also show NIFTy profiles with MAX-DOAS Averaging Kernels applied in the comparison.

In Figure 2, the geometric ray density decreases higher up the tower, which should lead to increased posterior uncertainty at upper levels. However, in Figure 4, the error bounds do not show a corresponding increase with altitude. The authors should clarify why the posterior uncertainty in Figure 4 remains relatively flat across altitude layers. Is the Bayesian framework underestimating uncertainty at higher levels due to overly confident prior assumptions?

While NO2 generally provides a strong differential absorption signal, I am wondering if this approach works for other weaker absorbers such as glyoxal in the same spectral region, where measurement uncertainties are substantially higher. And the manuscript does not discuss the operational limits of the their method when applied to lower signal-to-noise ratio data. The authors should include a dedicated discussion addressing the sensitivity and limitations of their approach regarding measurement noise. How does the NIFTy framework behave as measurement noise increases? Does a lower "SNR" cause the spatial reconstruction to collapse almost entirely onto the prior covariance functions, or does noise propagate into artificial spatial structures? How does full continuous Bayesian inference via NIFTy handle noise propagation and error covariance compared to typical Optimal Estimation Methods (OEM) or regularized least-squares (e.g., Tikhonov regularization) commonly used in DOAS profile retrievals? What are the "SNR" or measurement uncertainty thresholds beyond which the measurement information content is insufficient for a meaningful 2+1D spatial reconstruction?

Minor and Technical Comments

Figure 2: Axis labels and timestamps are extremely small and difficult to read. Please make sure the font size for labels in figures are consistent for the entire manuscript.

Please state the average computational run-time required for NIFTy to reconstruct a 24-hour dataset. Is this approach feasible for near-real-time data processing, or is it strictly a post-processing method?
Citation: https://doi.org/10.5194/egusphere-2026-2724-RC2

Manuel Henning, Philipp Haim, Stefan Schmitt, Johannes Lampel, Denis Pöhler, and Mark Wenig

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Short summary

This study presents a Bayesian framework for retrieving vertical NO₂ profiles from sparse measurements. By reconstructing a 2+1D spatiotemporal NO₂ density field using the NIFTy framework, height profiles are derived from combined long-path DOAS and in-situ measurements during the CINDI-III campaign. The reconstructed fields reproduce key atmospheric features and agree well with independent MAX-DOAS retrievals, demonstrating the feasibility of Bayesian inference for atmospheric tomography.


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A New NO2 Profile Retrieval from a Combination of Scanning Long-Path DOAS and Point Measurements Using Bayesian Inference-Based Spatiotemporal Reconstructions

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A New NO₂ Profile Retrieval from a Combination of Scanning Long-Path DOAS and Point Measurements Using Bayesian Inference-Based Spatiotemporal Reconstructions