Review of “Can radon help to improve methane emission estimates? Results from a dual-tracer inversion”

This manuscript aims to improve the reliability of CH₄ inversions through the inclusion of radon observations. The inversions are performed within the CarboScope framework, which is based on STILT footprints (at least in its standard configuration) and uses an iterative minimization of the cost function with a conjugate-gradient algorithm. The inversions are constrained by observations from 17 in-situ stations across Europe.

The authors use radon as an additional tracer to better characterize transport errors, particularly errors associated with vertical mixing within the planetary boundary layer. This is achieved by introducing correlations between CH₄ and Rn uncertainties in the observational uncertainty covariance matrix within a dual-tracer (CH₄–Rn) inversion framework. The model-data mismatches (MDMs) are estimated from prior model simulations and so-called “leave-one-out” runs.

The study further includes extensive sensitivity analyses, investigating different radon flux models, soil-moisture assumptions, and prior uncertainty settings for radon emissions. The authors discuss both the potential and the limitations of the proposed approach in a comprehensive and transparent manner.

The results indicate that including radon information in dual-tracer inversions generally leads to a smaller increase in CH₄ emissions over Central Europe compared to corresponding single-tracer CH₄ inversions.

Overall, this is an excellent study addressing one of the most important challenges in atmospheric inversions currently: transport uncertainty. Transport errors remain a major limitation for current greenhouse-gas inversions, and the presented work represents an interesting, feasible and scientifically sound contribution towards addressing this issue. The manuscript is comprehensive, methodologically rigorous, clearly written, and provides valuable insights. The authors build upon the well-established CarboScope framework and present a carefully designed experimental setup. I strongly recommend publication after a few minor issues have been clarified.

General comments

1. Lack of independent validation

One aspect that I find missing is an independent validation of the inversion results. As presented, it is difficult to assess whether the dual-tracer inversions actually provide more accurate CH₄ flux estimates than the single-tracer inversions. I fully acknowledge that obtaining an independent validation is challenging in practice. Nevertheless, would it be possible to compare prior and posterior MDMs at stations that are not assimilated in the inversion (at least during periods when the transport model is expected to perform reasonably well)? While such an analysis would still have limitations, it could provide at least some indication of whether the dual-tracer approach improves predictive skill.

2. Adjustments in regions with limited observational coverage

I was surprised by the sometimes substantial flux adjustments occurring in regions with sparse observational constraints, particularly over the Iberian Peninsula and parts of the Balkans. Do the footprints of the assimilated stations provide sufficient sensitivity to these regions to support such adjustments? I see similar behaviour occasionally in other inversion systems as well, something I never fully understood. It would be helpful if the authors could discuss this point and perhaps provide the observational sensitivity of the footprints in these regions.

3. Clarification of the leave-one-out experiments

It is not entirely clear to me whether the leave-one-out experiments are performed separately for each inversion setup or only once and subsequently reused across all inversion experiments. Based on the discussion around line 486 and following, I infer that they are repeated for each setup. Otherwise, it is difficult to understand how changes in the assumed prior uncertainty of radon emissions could lead to larger Rn MDMs that subsequently propagate to CH₄ through the cross-correlated uncertainties. I suggest clarifying this explicitly in the manuscript.

4. Definition of the observational covariance matrix in the dual-tracer inversion

Another point that is not entirely clear to me concerns the treatment of the diagonal elements of Qm. Do the diagonal variances remain identical in the dual-tracer inversion and the corresponding single-tracer inversion? If so, introducing the off-diagonal covariance terms effectively increases the total observational uncertainty represented by Qm, which would generally tend to reduce the strength of the inversion adjustments. Could part of the differences observed, for example for Germany in Fig. 6, be explained by this effect rather than by the transport-error information carried by radon itself?

Specific comments

Figure S2

It is somewhat surprising to me that several stations exhibit a substantial number of observations with strongly negative MDMs at very low mixing heights. Based on the common tendency of models to overestimate vertical mixing, I would have expected predominantly positive MDMs under such conditions.

This behaviour is particularly noticeable at WAO and MHD. For these coastal stations, could wind-direction errors also play an important role in addition to vertical mixing errors? For example, under low-wind conditions, especially during nighttime, the model may incorrectly advect emissions from the continent towards the station, whereas the station may in reality sample relatively clean marine background air.

Furthermore, what effect has the use of the modelled mixing height rather than observed mixing heights in this analysis? How well does the modelled mixing height compare to available observations?

Line 336

In addition, during nighttime there are generally no thermal upwinds along the slopes that would transport emissions from local sources towards mountain stations.

Maier et al perform a dual tracer CH₄ and ²²²Rn inversion, utilizing transport-induced correlations in the modeled time series of CH₄ and ²²²Rn to improve CH₄ flux estimates. The possibility of using ²²²Rn to trace the boundary layer dynamics in transport models and thereby quantify transport errors in a GHG inversion has long been considered a possibility, and the current effort follows earlier work from several coauthors on developing the components needed (Gachkivskyi et al., 2025; Karstens et al., 2015; Levin et al., 2021; Maier et al., 2025). I am heartened to see the progress and this eventual implementation of a dual tracer CH₄+²²²Rn inversion framework to address transport biases, a long-standing limitation of GHG inversions using boundary layer data.

The work itself is very thorough, and I have little to recommend by the way of improvements. The methods are clearly described, including the implementation of new features such as the off-diagonal Q_m matrix, and the authors have done an extensive set of sensitivity tests to quantify the different sources of error. This is an excellent study that should be published. The only clarification I would like is about their metric of judging whether a dual-tracer inversion is better than a single tracer, CH₄-only inversion. There are two issues, as follows.

Information flow due to off-diagonal elements in Q_m

The authors motivate their work by citing a seminal CO+CO₂ dual tracer inversion by Palmer et al (2006), in which both transport-induced correlations in Q_m and source-induced correlations in Q_p were implemented. As far as I understand that paper, Palmer et al (2006) did not see much improvements to CO fluxes in the dual tracer inversion (compared to the single tracer inversion). For CO₂ fluxes, the primary metric for judging that the dual tracer inversion was better was that it provided for a separation of NEE and biomass burning, as judged by their posterior correlation. They suggested that this was primarily due to CO:CO₂ transport correlations, since source correlations were too weak. This makes sense intuitively, since measurements of biomass burning CO plumes and enhancements could now provide information on how large the biomass burning CO₂ signal *should be* at those measurement locations. This would then be traced back to biomass burning CO₂ emissions, effectively separating it from NEE.

However, in their own work, the authors use the uncertainty reduction of CH₄ emissions as a metric of the added value of ²²²Rn measurements (lines 547—549, and again line 586). I do not understand why adding CH₄:²²²Rn correlations in Q_m would result in a stronger uncertainty reduction for CH₄ posterior emissions. In my mind, adding positive off-diagonal elements without changing the diagonals of Q_m should reduce the information content in the measurements. Take the extreme example of a correlation of +1 between two y-Hx. This means that two measurements could be collapsed into one without any loss of information, or reduction in the uncertainty of that average measurement. Then why does adding positive but <1 correlations in Q_m result in a stronger uncertainty reduction in methane emissions? I’m sure it does in the authors' setup (as they report), but I’m confused as to why. Some explanation of the flow of information here would be helpful.

Reduction of transport-induced bias

The authors motivate their work by citing the impact of transport biases on inversely estimated fluxes, especially the bias in venting the PBL into the free troposphere. However, as they themselves acknowledge, adding ²²²Rn as a second tracer does not “fix” the transport biases. Following their logic, it’s not clear to me that ²²²Rn observations would in any way reduce the transport-induced bias in posterior fluxes. If anything, by sampling a biased transport model more, the additional observations would solidify the bias in the flux estimates. If that’s the case, then what is the added benefit of adding a transport tracer such as ²²²Rn to the inverse model? Palmer et al (2006) benefited from adding CO observations and CO:CO₂ correlations because there were more CO observations than CO₂ observations, and the added correlation could provide information about CO₂ fluxes from CO enhancements. However, that is not the case here, because ²²²Rn is more difficult to measure than CH₄, so there are not more ²²²Rn measurements than CH₄. How do the additional ²²²Rn measurements then mitigate the transport bias effect on CH₄ estimates, that the authors state as a motivating factor? In any case, the metric for checking such a benefit would not be uncertainty reduction, but rather distance from true emissions in an OSSE.

References

Gachkivskyi, M., Karstens, U., Fischer, B., Kubistin, D., Müller-Williams, J., Lindauer, M., and Levin, I.: Radon-222 monitoring at German ICOS atmosphere stations, Earth Syst. Sci. Data, 17, 6173–6197, https://doi.org/10.5194/essd-17-6173-2025, 2025.

Karstens, U., Schwingshackl, C., Schmithüsen, D., and Levin, I.: A process-based ²²²radon flux map for Europe and its comparison to long-term observations, Atmospheric Chem. Phys., 15, 12845–12865, https://doi.org/10.5194/acp-15-12845-2015, 2015.

Levin, I., Karstens, U., Hammer, S., DellaColetta, J., Maier, F., and Gachkivskyi, M.: Limitations of the radon tracer method (RTM) to estimate regional greenhouse gas (GHG) emissions – a case study for methane in Heidelberg, Atmospheric Chem. Phys., 21, 17907–17926, https://doi.org/10.5194/acp-21-17907-2021, 2021.

Maier, F., Falge, E., Gachkivskyi, M., Henne, S., Karstens, U., Kikaj, D., Levin, I., Manning, A., Rödenbeck, C., and Gerbig, C.: How reliable are process-based ²²²radon emission maps? Results from an atmospheric ²²²radon inversion in Europe, Atmospheric Chem. Phys., 25, 12779–12809, https://doi.org/10.5194/acp-25-12779-2025, 2025.

Palmer, P. I., Suntharalingam, P., Jones, D. B. A., Jacob, D. J., Streets, D. G., Fu, Q., Vay, S. A., and Sachse, G. W.: Using CO₂:CO correlations to improve inverse analyses of carbon fluxes, J. Geophys. Res. Atmospheres, 111, n/a--n/a, https://doi.org/10.1029/2005JD006697, 2006.