Determining optimal model height to represent mountain observations in atmospheric transport and inversion studies

Dahl, Lilja; Vojta, Martin; Pisso, Ignacio; L. Thompson, Rona; Bigi, Alessandro

doi:10.5194/egusphere-2026-2734

Preprints

https://doi.org/10.5194/egusphere-2026-2734

Preprints

11 Jun 2026

| 11 Jun 2026

Determining optimal model height to represent mountain observations in atmospheric transport and inversion studies

Lilja Dahl, Martin Vojta, Ignacio Pisso, Rona L. Thompson, and Alessandro Bigi

Abstract. Accurate modelling atmospheric transport over complex terrain is challenging due to processes interacting with the orography and the use of finite resolution wind fields in Atmospheric Transport Models (ATMs). An unresolved issue is the representation of mountain stations within ATMs, and particularly the choice of model height that best represents mountain observations. This study proposes a methodology to determine optimal heights for representing mountain sites in ATMs, using FLEXPART driven by ECMWF ERA5 wind fields at two spatial resolutions. Three different release height methods were evaluated: i) sampling inlet height (S-rh), ii) an intermediate height based on model orography (P-rh), and iii) a varying release height determined by matching ERA5 potential temperature with observations (T-rh). A sensitivity analysis is presented, determining the optimal particle release height for three mountain sites and its influence on the simulated mixing ratios, using SF₆ as a tracer and two prior fluxes across different seasons and diurnal cycles. Results show that the model performance strongly depends on the release height choice, spatial resolution of the wind fields, station characteristics and atmospheric condition. The varying T-rh, generally provided a good representation of the observations across seasons and sites, although summer advection was not well captured. S-rh systematically underestimated observed variability, leading to a weaker source-receptor relationship (SRR) and biased posterior emissions. These findings highlight the importance of representing mountain stations in ATMs to reduce the model-data mismatch and that an inappropriate release height can lead to systematic bias of posterior flux estimates.

Received: 13 May 2026 – Discussion started: 11 Jun 2026

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Lilja Dahl, Martin Vojta, Ignacio Pisso, Rona L. Thompson, and Alessandro Bigi

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-2734', Anonymous Referee #1, 19 Jul 2026
General Comment
The paper proposes a new methodology to determine the optimal height for representing mountain sites in atmospheric transport models. The methodology is tested using the Lagrangian particle dispersion model FLEXPART driven by ERA5 reanalysis, performing a sensitivity analysis for three mountain sites in the European Alps, using SF₆ as a tracer.
The topic is interesting, potentially valuable to the scientific community, and well aligned with the scope of Atmospheric Chemistry and Physics. However, in my opinion, the manuscript in its current form does not meet the journal’s quality standards, particularly with regard to the methodology and the presentation of the results. The latter is difficult to follow and consists largely of an extensive comparison of statistical metrics, with limited physical interpretation.
Specific Comments
The Authors decided to use ERA5 reanalysis fields to drive FLEXPART. The reasons for this choice are weakly explained in the manuscript. Moreover, it is unclear how the Authors derived the ERA5 fields at two different horizontal grid spacings (0.5°x0.5° and 0.2°x0.2°). As far as I know, ERA5 reanalysis presents an original horizontal grid spacing of about 31 km (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-complete?tab=overview). Therefore, it is unclear, particularly for the higher-resolution 0.2° × 0.2° grid, how the fields were obtained, as this is not explained in the manuscript. This lack of information hinders the interpretation of the results.

The Authors in Section 2.3 try to explain the rationale for the choice of the grid points closest to the three mountain sites. I think I have not completely grasped the problems they encountered in matching ERA5 coordinates with station coordinates. However, from Table 2, it seems strange to me that the altitude of the two high-altitude stations is lower in the higher-resolution dataset than in the coarser-resolution dataset. Moreover, it is still unclear how the higher-resolution orography was derived, starting from the original ERA5 orography.

It is not completely clear to me how the proxy release height (P-rh) was calculated

In Section 2.2.2, it is written “at mountain sites, θ increases monotonically with height and can therefore be used as a vertical coordinate”. Actually, this is not always true. It is true that the free atmosphere is most of the time stably stratified and therefore the potential temperature increases with height, but sometimes unstable stratification can be present. I suppose that this can occur, for example, at the low-elevation station (Schauinsland). In the same section, it is written that the pressure in ERA5 “fluctuated beyond acceptable limits”. What exactly does this mean, and how were these acceptable limits defined?

In my opinion, the presentation of the results is difficult to read and is limited to a long list of evaluation metrics, without an in-depth discussion or physical interpretation of the results. Moreover, by the end of the results section, it remains unclear, at least to me, what advantages or added value the proposed new methodology offers for determining the optimal height at which mountain sites should be represented.

Technical corrections
Lines 58-59: the second part of the sentence “and ATM might not have a suitable turbulence parameterization…” is not related to the first part.
Lines 63-64: potential temperature is conserved in adiabatic conditions, not always.
Line 88: “stochastic turbulent and diffusive transport”
Lines 91-93: The pronouns and verbs should be plural rather than singular, as the subject is “LPDMs.”
Lines 135-136: “Atmospheric observations…were collected”
Line 151: Why is the wind field at 0.2°x0.2° spatial resolution missing in December?
Line 165: for consistency, it should be “the geopotential height of Zt and Zs”
Line 171: actually, 1000 hPa is typically used as the reference pressure in the definition of potential temperature (https://glossary.ametsoc.org/wiki/potential-temperature/).
Line 196: Figure 2 does not show “a contour of the ERA5 orography of the three mountain sites”, but rather the ERA5 orography of the Alps.
Line 225: “we run 30 iterations…”
Line 244: something is missing at the end of the sentence.
Line 271: the lowest MBE.
Lines 282-283: “T-rh showed greatest…in comparison to T-rh”. The initial or final T-rh is wrong in this sentence.
Line 311: the reference to the section is missing.
Line 316: “exhibited slightly higher σ_n values”.
Lines 329-333: this is a long sentence difficult to follow.
Line 347: “The results of the atmospheric inversions presented in Fig. 12 show…”
Line 349: “at two spatial resolutions”.
Line 368: “and choosing an inappropriate…”
Lines 380-381: “using” is repeated.
Citation: https://doi.org/10.5194/egusphere-2026-2734-RC1
RC2:
'Review of egusphere-2026-2734', Anonymous Referee #2, 25 Aug 2026
The study by Dahl et al. addresses the important question of atmospheric model representativeness at mountain stations, here with respect to atmospheric composition and more specifically greenhouse gas concentrations. Due to limited horizontal model resolution mountain top observations are difficult to match in the model. Different strategies for selecting the best "sampling height" in model data have been used in the past. Here, the authors suggest using a variable "sampling height" that is based on observed and simulated potential temperatures. The suggested method is plausible and could be a valuable contribution to numerous studies on atmospheric composition including inverse model. As such it should be of interest to the readers of ACP. However, there are several points I would like the authors to address to clarify their results.
The manuscript is relatively broad, introducing a new strategy for selecting a representative model height above ground from comparison of observations from sites in mountainous terrain, validating this method with 'forward' simulations of an SF6 tracer and finally demonstrating the impact on inverse modelling of emissions of the same tracer. Being this broad a lot of detail seems to be missing from the presentation and discussion of results that would help the reader to assess the benefits of the newly introduced model height selection. This essentially leads to the next two points.

I am missing a thorough justification of the height selection method and a discussion of its limitations also with respect to its theoretical foundation. The assumption of adiabatic conditions is not questioned at all but seems to limit the successful application.

Which leads to my final major concern. There is no compelling demonstration of the general benefits of the temperature-based height selection method. At least not for the selected tracer, which, due to its source distribution and connected uncertainties, might not have been the best choice for demonstrating the new method.

These points are picked up in the specific comments below and suggestions are made for improving the manuscript, which in my view requires major modifications before it can be published in ACP.

Specific comments
Line 27: The Vojta study seems very specific in the context of introducing global scale atmospheric greenhouse gas inversions. It would make more sense to mention efforts like the global carbon project and associated publications.
L29: Nothing wrong with Bergamaschi et al. being a continental-scale study, but it is not related to the mentioned Horizon Europe projects. Better examples for PARIS and AVENGERS would be: https://acp.copernicus.org/articles/26/7647/2026/ and https://gmd.copernicus.org/articles/18/1505/2025/
L33: Munassar et al. is not UK-specific. It is another continental scale study from the VERIFY project and would fit better to the HEU projects mentioned above.
L39f: Why mention two specific LPDMs when citing something general about Eulerian transport? Would be better to cite something general about LPDMs here as well (e.g., Lin et al 2012: https://doi.org/10.1029/2012GM001376) or the classical Thompson 1987 contribution which is cited later).
Paragraph starting L60: This paragraph does not flow well. It starts with "several studies" and then only cites one. Please extend to several studies or reword. For example, there are several studies from the US and Europe that looked at the impact of different resolution LPDMs on inverse modelling in complex terrain (Karion et al., 2019, 10.5194/acp-19-2561-2019; Katharopoulos et al., 2023, 10.5194/acp-23-14159-2023). Then the paragraph continues with a break and the concept of using potential temperature as vertical coordinate is introduced. This should be a separate paragraph.
L63f: The current statement suggests that potential temperature is a generally conserved quantity in the atmosphere, which is not the case. It is only conserved during adiabatic processes. Flow over surfaces might not be adiabatic because of heat exchange with the surface (thermally driven wind systems in mountain terrain would be very much subject to such fluxes). Furthermore, flow over mountains is often connected with cloud/rain formation. Again, a process that is not adiabatic. These limitations need to be discussed from the beginning. They are also not mentioned later when results are presented.
L75: There is very little justification given for selecting SF6 as a target tracer. There are other suitable tracers (CO, CH4, widely-used HFCs like HFC-134a mention in the conclusions) for which emissions are better known and that are observed at many mountain sites. It is known from other studies that SF6 has a large point-source in south-western Germany, which, especially, makes the interpretation of the presented results for SSL difficult (see Vojta et al., 2024 and Meixner et al., 2025, https://doi.org/10.1021/acsestair.5c00234). There is no mention of difficult source situation anywhere in the manuscript. I would have been a good idea to look at multiple tracers as this would allow checking consistency of the approach.
L100: The terminology is a bit confusing. Is $H^bkg$ simply the surface sensitivity in a larger domain or really a sensitivity to a background mole fraction? I suspect it is the first, in which case I would rather refer to it as $H^main$ (following FLEXPART terminology) or $H^global$.
Equation 1: The rightmost part of the equation seems to omit the initial mole fractions. Either remove it or reformulate … = H(x) + yini
L109: Isn't the nominal resolution of ERA5 only about 36 km in central Europe? So, extracting to 0.2°x0.2° is already increasing this resolution by interpolation, right? This needs to be mentioned.
L151: Why would these be missing? ERA5 is a continuous dataset.
Table 2: This is a rather incomplete table caption. Please be a bit more explicit and describe what is contained in the table. Rather than describing this in the text, put it into the table caption. Columns lon and lat are missing information about units. Reader has to guess that these are degrees East and degress North.
L166: The statement about theta vertical profiles seems a bit too generalised. Maybe this is true for mountain top sites, but certainly not for mountain sites in general. Decreasing theta with height would be a sign of unstable atmospheric stratification and as such occurs near the surface during periods of positive (into the atmosphere) heat flux. This might be rare at an isolated mountain top, but a site like SSL is not that isolated and unstable conditions are likely to occur during summer daytime. Please consider in the discussion of results and reword here.
L171 reference pressure: I disagree. Commonly ps is called p0 and a value of 1000 hPa is used: https://glossary.ametsoc.org/wiki/potential-temperature/. Also, the use of a model surface pressure instead of a constant value is odd. However, it should not impact the result as long as the same ps was applied to the model data as well as to the observations at the same time.
L174f: 'certain stations fluctuated beyond acceptable limits': This sounds very vague. What does "certain stations" mean and what are the "acceptable" limits? Is this mainly for the site SSL, where ambient temperatures are more impacted by local heat flux (see comment above)?
L177: So, this pressure may be smaller than the station pressure (release height above real station altitude)? Again, is this something that only occurs at SSL (as suggested in Fig. 10b), which again would indicate the impact of unstable situations on the T-rh approach.
L180, reference to Figures A1-A4: These figures could be interesting if they would be discussed in any detail in the text, better would be a discussion of some statistical parameters describing the shown parameters. For example, the only information the reader gets about the differences of the finally calculated release heights is in Table 3, where only a median and quantile range for T-rh is given.
Table 3: Why does the table only contain 4 months? If I understand correctly, T-rh was calculated for all months of 2019 (exception higher-resolution ER5 in December).
Table 3: The values seem to suggest that for JFJ and ZSF the lower resolution ERA5 topography requires a smaller release height above ground than the higher resolution ER5 orography. This is the case for all three release sites. The opposite would have been intuitive (higher resolution topography -> closer match to real topography).
L187ff: This paragraph seems a bit lost after the main results (median release heights) have already been mentioned. I also wonder if this level of detail is required. The isothermal hypsometric equation is textbook knowledge and as such does not need to be repeated here. A similar argument might be used to omit definition of potential temperature (Eq. 2).
Section 2.3: If I understand this section correctly, the grid cell with the smallest altitude mismatch is chosen for the calculation of T-rh, right? This approach is a bit odd. FLEXPART and other LPDMs usually use bi-linear (or higher order) interpolation when receiving variables at particle locations. Hence, I would have expected that the whole discussion about orography mismatch and calculating theta profiles would be based on the interpolated model orography and other variables at the exact station location.
L244: The sentence is incomplete. There is also no description of Table 4. Table 4 in itself is a bit confusing. It seems to introduce 3 sensitivity inversions (one for each release height approach), but then it gives single values in all other columns, which suggests that a table is not needed here, but values could be mentioned in the text. There seems to be a contradiction about the prior as well. Text states that it is EDGAR v8, whereas the table and section 2.5 suggest that it is combination of EDGAR with a posteriori results form previous studies. Finally, it remains unclear if the inversions make use of the complete European SF6 observing network or only of the three sites discussed in the context of release heights (Figure A5 seems to suggest that latter). If it is only the subset of three sites, it is necessary to discuss the comparability of the results with respect to recent inversion studies that used a more complete set of observations (Vojta et al., 2024 and Meixner et al., 2025). If it is only three (mountain) sites it would be good to mention that the resulting posterior differences for the different release heights most like represent the maximal impact of release height since in a more complete inversion setup additional sites in flat terrain would be utilised as well and dampen the influence of mountain sites.
L255f: As this describes the content of one or several figures a reference to an example figure should be added.
L259f: It is well known that observed local wind directions may deviate strongly from simulations due to local channeling effects. JFJ is an extreme case for such a mismatch as it sits on a saddle point between two larger mountains and not at an isolated peak. Please consider in the discussion. Unfortunately, there is no further mention of such an analysis in the remainder of the manuscript or is this referring to the analysis presented in section 3.1? Then I would rather introduce these as case studies and not a result of a systematic wind analysis, which to me would suggest something else than the discussion of two short episodes.
Section 3: This section needs additional structure and possibly restructuring. It starts without a subsection but should rather have one called something like 'Statistical performance analysis of SF6 simulations'. To me it would also make more sense to start with the case studies, which indicate the specific importance of release height and then go to the more general analysis/conclusions.
Fig 5 and similar: It is difficult to discern the seasonality aspect in the figures as it seems to be indicated by the border color only (information missing in caption). Displaying three different aspects in the symbols is somewhat overloading the plot. Maybe using different symbol sizes would work better than different border colors. Omitting one of the aspects may be a good solution as well. Right now, the different colors dominate the figures, but bias might be the least important aspect in the comparison. Alternatively, all statistical metrics could be included in a table or in a bar chart.
L264: The question of free troposphere versus boundary-layer influenced was discussed frequently for many mountain sites. Rather than stating predominantly free troposphere, the problem of the intermittent influences should be mentioned (e.g. Herrmann et al., 2015, 10.1002/2015JD023660). The preferable notation would be predominantly in the free troposphere with frequent influences from the planetary boundary layer during the warm season. This is true for JFJ and ZSF, but not necessarily for SSL with its smaller prominence over the surrounding terrain.
L285: What is implied by stating 'good performance'? I don't think that Figure 5 shows that T-rh outperforms the two other methods in general. This is especially true for the higher-resolution case and night-time observations (those that people tend to assimilate in inversions).
L311: "Sect xxx". Section reference missing.
L311: "weak correlation": How would a constant offset change the correlation? I would rather think that the location is too challenging for any low-resolution model to capture the complex daytime dynamics of advection from the Rhine valley. The other problem with SSL and SF6 might be the relative short distance to the recently identified major source SF6 in south-western Germany (see Vojta et al., 2024 and Meixner et al., 2025). Did the performance for SSL improve when the optimised SF6 fluxes were used in the simulations?
L332: It is a bit difficult to see, but I assume the simulated "spurious" peaks in Fig 8a relate to the times when the T-rh release height was below the MLH? As stated, these are likely very stable situation in which we would expect a relatively strong increase in potential temperature with height. How is it possible that T-rh then produces such low release heights? I suspect that the local observed temperature at ZSF must have been impacted by local cooling (cold pool formation) and not have been representative for the free tropospheric temperature (gradient).
L334: It is not clear why a case is discussed where the methods do not differ much. Wouldn't it be more interesting to show a case where larger differences occur. Fig 8b suggests that at 0.2° resolution the peaks differ quite a bit, but it is unclear if Fig 9 shows simulations based on 0.2 or 0.5° simulations. Judging from the step between the wind arrows, it is the coarser resolution version, for which things agreed, but more interesting would be a plot of the higher resolution footprints for which the SF6 mole fractions did not agree as well.
L339: Why was this time chosen? Is this just before the first peak was observed on 2019-10-24?
L340: If release height is the only parameter that was changed between simulations, it is not surprising that it is predominating the SRR differences. I think what you want to express is that given the observed convergence zone, it is not surprising that the release height has such a strong impact on SRRs. Rephrase.
L347: Something wrong with this sentence is: '... presented in Fig. 12 shows ...' Rephrase.
L359 and 363: Negative fluxes (unphysical for SF6) or negative posterior increments?
L366f: This is a difference of 1.5 %. How does that compare to other uncertainties in the inversion system and to the analytical posterior uncertainty?
Table 6: These are odd units! Why not use Gg yr-1 instead the 10^-5 notation?
Figure 12: Caption needs to explain that this is the increment posterior - prior. Otherwise, it might be mistaken for a temporal increment.
L371f: This first sentence of the conclusions seems to omit the main focus of the paper: different release heights for mountain sites. Also, the focus on Northern Italy seems new (first mention here). Please rephrase.
L393f: This is very much within the general expectation. More interesting would be the question if such a bias is larger than the overall inversion uncertainty and if it would be largely avoided by the commonly used P-rh release height.
L402: Another point the outlook could mention is that more high-resolution model products have become or will become available, e.g. ERA6 will have a nominal resolution of 14 km in Central Europe and national weather services already provide analysis products at kilometer-scale resolution (DWD ICON-DREAM). This may reduce the release-height problem.
Supplement Figures A6-A7 are not mentioned in the main text. What is their purpose?
Code availability: Has the theta-based release height been implemented in this FLEXPART version or is it based on pre-processing code. Such updated version or standalone code should be made available as well.
Citation: https://doi.org/10.5194/egusphere-2026-2734-RC2

Lilja Dahl, Martin Vojta, Ignacio Pisso, Rona L. Thompson, and Alessandro Bigi

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Short summary

This study addresses the challenge of accurately representing mountain observations in Atmospheric Transport Models and inverse modeling studies. We introduce a new varying release height method based on potential temperature to better represent mountain observations in the ATM. We evaluated three release height methods at three mountain sites and the results show that the model performance strongly depends on the release height choice, meteorological resolution, and atmospheric conditions.


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