Implementation of a sigma coordinate system in PALM-Sigma v1.0 (based on PALM v21.10) for LES study of the marine atmospheric boundary layer

Ning, Xu; Bakhoday-Paskyabi, Mostafa

doi:10.5194/egusphere-2025-4390

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https://doi.org/10.5194/egusphere-2025-4390

Preprints

06 Oct 2025

| 06 Oct 2025

Implementation of a sigma coordinate system in PALM-Sigma v1.0 (based on PALM v21.10) for LES study of the marine atmospheric boundary layer

Xu Ning and Mostafa Bakhoday-Paskyabi

Abstract. In large-eddy simulation studies of the marine atmospheric boundary layer, wind–wave interactions are often oversimplified using wall-stress models parameterized by roughness length, overlooking the complex coupling dynamics, especially under wind–wave non-equilibrium. Here, we develop a new LES solver based on the PALM model architecture that employs a surface-following sigma-coordinate system to explicitly resolve evolving wave geometry. Simulations under low-wind conditions with different wave regimes reproduce characteristic features of wave-driven winds reported in previous studies. Notably, the results show that wave-induced form stress significantly modulates vertical momentum flux, with effects extending well beyond the wave boundary layer. Leveraging PALM’s parallelized framework, the solver can be integrated with existing multi-scale nesting and coupled with wave models. This high-fidelity modeling tool advances the understanding and parameterization of wind–wave coupling under realistic met-ocean conditions.

Received: 08 Sep 2025 – Discussion started: 06 Oct 2025

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Journal article(s) based on this preprint

03 Mar 2026

Implementation of a sigma coordinate system in PALM-Sigma v1.0 (based on PALM v21.10) for LES study of the marine atmospheric boundary layer

Xu Ning and Mostafa Bakhoday-Paskyabi

Geosci. Model Dev., 19, 1769–1789, https://doi.org/10.5194/gmd-19-1769-2026,https://doi.org/10.5194/gmd-19-1769-2026, 2026

Short summary

Xu Ning and Mostafa Bakhoday-Paskyabi

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4390', Anonymous Referee #1, 03 Nov 2025
Synopsis:
The authors Xu Ning and Mostafa Bakhoday-Paskyabi report in their manuscript entitled “Implementation of a sigma coordinate system in PALM-Sigma v1.0 (based on PALM v21.10) for LES study of the marine atmospheric boundary layer” on the development of a large‑eddy‑simulation (LES) code based on the PALM LES framework, incorporating a modified vertical coordinate that accounts for the actual, instantaneous position of the atmospheric lower boundary. The authors use their code to investigate the interaction of the wave‑induced effect between surface waves and the marine atmospheric boundary layer. Their results clearly demonstrate that the modelling approach commonly employed in atmospheric flow models—representing the ocean’s influence on the atmosphere solely through a roughness length parameterized as a function of wave characteristics such as significant wave height and wave period—constitutes a strong simplification, especially in situations where the wave field is not in equilibrium with the wind field. For example, the authors show that the mismatch between wave direction and wind direction also influences properties of the marine atmospheric boundary layer above the wave‑affected layer. When wind and waves are opposed, turbulence throughout the entire marine atmospheric boundary layer is enhanced compared to the case where wind and waves are aligned.
Evaluation:
I would like to thank the authors for what I consider to be an excellent piece of work. The manuscript is both very well structured and very well written. I have only minor comments on the manuscript, and therefore I recommend its acceptance for publication in EGUsphere after minor revisions. I’ll ask the authors to take the comments below into account when revising the manuscript.
Comments:
Page 1, line 24/25: “The latest high-performance computing (HPC) equipment enables numerical simulations with a magnitude of grid points up to 1010 (Kröniger et al., 2018)” I suggest to find a more recently published paper as a reference for the number of grid points that can be handled by the latest generation of HPC clusters. I think it is slightly contradictory if you speak of latest HPC equipment (which should be from 2025), but refer to a paper from 2018. If no more recent publication is available I suggest to modify the sentence, e.g. as follows: “Already in 2018 high-performance computing (HPC) equipment enabled numerical simulations with a magnitude of up to 10°10 grid points (Kröniger et al., 2018)”.

Page 2, line 27: Please correct “In numerical modeling of the marine atmospheric boundary layer flows” to “In numerical modeling of marine atmospheric boundary layer flows”.

Page 3, line 68: Please change “The current work further develop PALM …” to “The current work further develops PALM …”.

Page 8, equation 23: The values of the weights applied in the Runge-Kutta scheme should be specified.

Page 12, line 246: To apply the grid stretching already inside the atmospheric boundary layer is rather uncommon at least in work that has been done with the LES code PALM. Typically, the grid stretching would be applied above the atmospheric boundary-layer where turbulent processes do not play a major role any longer. It would be an extremely interesting result if the authors could show that applying the grid stretching already inside the boundary layer does not change the results significantly as it would be of importance for the computing resources required to carry out LES runs. Therefore, I ask the authors to extend their study by one extra simulation that applies a uniform distance in z-direction inside the boundary layer.

Page 12, line 247: The authors report that their model domain has a size of 1200 m x 1200 x 850 m. The initial height of the bottom boundary of the inversion layer chosen by the authors is 600 m. I’m wondering whether the size of the model domain is actually large enough. I ask the authors to add a statement whether they checked the sensitivity of their results on the size of the model domain.

Page 12, line 249: The authors report that they have applied a total simulation time of 20 h. Is that length of the simulation run sufficient to get rid of the inertial oscillations that occur in simulations with PALM if the Coriolis force is switched on? g. Maas (2023) used a physical simulation time of 48 h to obtain a steady-state mean flow in his LES of an offshore flow at 55°N (Maas, 2023: From gigawatt to multi-gigawatt wind farms: wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations).In order to allow others to repeat their simulations the authors should provide also an information on which geographical latitude was assumed in their simulations. Moreover, information on the lateral boundary conditions chosen should be provided. Page 14, figure 3: I doubt slightly the value of showing a comparison of instantaneous velocity fields. The flow is anyhow different. We do not see the impact of background turbulence and turbulence created by the different surface waves.- I think to show statistical measures like the variance of velocity components makes more sense

Page 15, figure 4: The caption of figure 4 lacks an information which cases are actually shown in the figure.

General comment: I encourage the authors to mention also other possible applications of their modified PALM code such as flow in complex terrain in the outlook section of their manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4390-RC1
- AC2: 'Reply on RC1', Xu Ning, 17 Jan 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4390-AC2
RC2:
'Comment on egusphere-2025-4390', Anonymous Referee #2, 09 Nov 2025
The authors present the implementation of a sigma coordinate system in the LES code PALM and show its application to the marine atmospheric boundary layer. The authors show how their code development significantly improves the representation of the interaction between a wavy water surface and the marine boundary layer. Their comparison between different cases with and without waves with and without movement is done with great detail and reveals significant changes in the mean properties and the turbulent structure of the marine boundary layer if the new sigma coordinate system is used with moving waves. Their findings also agree with other results reported in the literature. Therefore, I recommend accepting the manuscript for publication in EGUsphere. However, I would like to ask the authors to consider the following comments.

p.3, l.63: "PALM" should be used as a fixed name, not as an abbreviation as stated in Maronga et al. (2020).

p.3, l.87: theta_v stands for the *virtual* potential temperature (in Table 1, it is already correctly defined).

p.10, l.222: "In parallel, it updates the wave field [...]" I doubt that this happens in parallel (meaning that a part of the computing units does the update of the wave fields while other units integrate the prognostic equations) but more likely one after the other.

p.10, l.227: "Finally, all simulation data ware written to output files." In standard PALM, this is done within the time-stepping loop to allow, e.g., hourly data output.

Fig.1: The figure does not show what is written in the text. On the left, the pressure solver and the prognostic solver should be switched. The Boundary-condition update is not mentioned in the text. Also, the flow structure is not that well represented. I recommend updating the figure to better show the program structure. An example would be Fig. 10 in Maronga et al. (2015, doi:10.5194/gmd-8-2515-2015) which shows the flowchart of an older version of PALM.

p.13, l.279: From my understanding of the figures, the words "windward" and "leeward" should be swapped in this sentence.

Fig.4: Please add which cases are represented in each row.
Citation: https://doi.org/10.5194/egusphere-2025-4390-RC2
- AC1: 'Reply on RC2', Xu Ning, 03 Jan 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4390-AC1
RC3:
'Comment on egusphere-2025-4390', Lichuan Wu, 24 Nov 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-RC3-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-4390-RC3
- AC3: 'Reply on RC3', Xu Ning, 26 Jan 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4390-AC3

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4390', Anonymous Referee #1, 03 Nov 2025
Synopsis:
The authors Xu Ning and Mostafa Bakhoday-Paskyabi report in their manuscript entitled “Implementation of a sigma coordinate system in PALM-Sigma v1.0 (based on PALM v21.10) for LES study of the marine atmospheric boundary layer” on the development of a large‑eddy‑simulation (LES) code based on the PALM LES framework, incorporating a modified vertical coordinate that accounts for the actual, instantaneous position of the atmospheric lower boundary. The authors use their code to investigate the interaction of the wave‑induced effect between surface waves and the marine atmospheric boundary layer. Their results clearly demonstrate that the modelling approach commonly employed in atmospheric flow models—representing the ocean’s influence on the atmosphere solely through a roughness length parameterized as a function of wave characteristics such as significant wave height and wave period—constitutes a strong simplification, especially in situations where the wave field is not in equilibrium with the wind field. For example, the authors show that the mismatch between wave direction and wind direction also influences properties of the marine atmospheric boundary layer above the wave‑affected layer. When wind and waves are opposed, turbulence throughout the entire marine atmospheric boundary layer is enhanced compared to the case where wind and waves are aligned.
Evaluation:
I would like to thank the authors for what I consider to be an excellent piece of work. The manuscript is both very well structured and very well written. I have only minor comments on the manuscript, and therefore I recommend its acceptance for publication in EGUsphere after minor revisions. I’ll ask the authors to take the comments below into account when revising the manuscript.
Comments:
Page 1, line 24/25: “The latest high-performance computing (HPC) equipment enables numerical simulations with a magnitude of grid points up to 1010 (Kröniger et al., 2018)” I suggest to find a more recently published paper as a reference for the number of grid points that can be handled by the latest generation of HPC clusters. I think it is slightly contradictory if you speak of latest HPC equipment (which should be from 2025), but refer to a paper from 2018. If no more recent publication is available I suggest to modify the sentence, e.g. as follows: “Already in 2018 high-performance computing (HPC) equipment enabled numerical simulations with a magnitude of up to 10°10 grid points (Kröniger et al., 2018)”.

Page 2, line 27: Please correct “In numerical modeling of the marine atmospheric boundary layer flows” to “In numerical modeling of marine atmospheric boundary layer flows”.

Page 3, line 68: Please change “The current work further develop PALM …” to “The current work further develops PALM …”.

Page 8, equation 23: The values of the weights applied in the Runge-Kutta scheme should be specified.

Page 12, line 246: To apply the grid stretching already inside the atmospheric boundary layer is rather uncommon at least in work that has been done with the LES code PALM. Typically, the grid stretching would be applied above the atmospheric boundary-layer where turbulent processes do not play a major role any longer. It would be an extremely interesting result if the authors could show that applying the grid stretching already inside the boundary layer does not change the results significantly as it would be of importance for the computing resources required to carry out LES runs. Therefore, I ask the authors to extend their study by one extra simulation that applies a uniform distance in z-direction inside the boundary layer.

Page 12, line 247: The authors report that their model domain has a size of 1200 m x 1200 x 850 m. The initial height of the bottom boundary of the inversion layer chosen by the authors is 600 m. I’m wondering whether the size of the model domain is actually large enough. I ask the authors to add a statement whether they checked the sensitivity of their results on the size of the model domain.

Page 12, line 249: The authors report that they have applied a total simulation time of 20 h. Is that length of the simulation run sufficient to get rid of the inertial oscillations that occur in simulations with PALM if the Coriolis force is switched on? g. Maas (2023) used a physical simulation time of 48 h to obtain a steady-state mean flow in his LES of an offshore flow at 55°N (Maas, 2023: From gigawatt to multi-gigawatt wind farms: wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations).In order to allow others to repeat their simulations the authors should provide also an information on which geographical latitude was assumed in their simulations. Moreover, information on the lateral boundary conditions chosen should be provided. Page 14, figure 3: I doubt slightly the value of showing a comparison of instantaneous velocity fields. The flow is anyhow different. We do not see the impact of background turbulence and turbulence created by the different surface waves.- I think to show statistical measures like the variance of velocity components makes more sense

Page 15, figure 4: The caption of figure 4 lacks an information which cases are actually shown in the figure.

General comment: I encourage the authors to mention also other possible applications of their modified PALM code such as flow in complex terrain in the outlook section of their manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4390-RC1
- AC2: 'Reply on RC1', Xu Ning, 17 Jan 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4390-AC2
RC2:
'Comment on egusphere-2025-4390', Anonymous Referee #2, 09 Nov 2025
The authors present the implementation of a sigma coordinate system in the LES code PALM and show its application to the marine atmospheric boundary layer. The authors show how their code development significantly improves the representation of the interaction between a wavy water surface and the marine boundary layer. Their comparison between different cases with and without waves with and without movement is done with great detail and reveals significant changes in the mean properties and the turbulent structure of the marine boundary layer if the new sigma coordinate system is used with moving waves. Their findings also agree with other results reported in the literature. Therefore, I recommend accepting the manuscript for publication in EGUsphere. However, I would like to ask the authors to consider the following comments.

p.3, l.63: "PALM" should be used as a fixed name, not as an abbreviation as stated in Maronga et al. (2020).

p.3, l.87: theta_v stands for the *virtual* potential temperature (in Table 1, it is already correctly defined).

p.10, l.222: "In parallel, it updates the wave field [...]" I doubt that this happens in parallel (meaning that a part of the computing units does the update of the wave fields while other units integrate the prognostic equations) but more likely one after the other.

p.10, l.227: "Finally, all simulation data ware written to output files." In standard PALM, this is done within the time-stepping loop to allow, e.g., hourly data output.

Fig.1: The figure does not show what is written in the text. On the left, the pressure solver and the prognostic solver should be switched. The Boundary-condition update is not mentioned in the text. Also, the flow structure is not that well represented. I recommend updating the figure to better show the program structure. An example would be Fig. 10 in Maronga et al. (2015, doi:10.5194/gmd-8-2515-2015) which shows the flowchart of an older version of PALM.

p.13, l.279: From my understanding of the figures, the words "windward" and "leeward" should be swapped in this sentence.

Fig.4: Please add which cases are represented in each row.
Citation: https://doi.org/10.5194/egusphere-2025-4390-RC2
- AC1: 'Reply on RC2', Xu Ning, 03 Jan 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4390-AC1
RC3:
'Comment on egusphere-2025-4390', Lichuan Wu, 24 Nov 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-RC3-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-4390-RC3
- AC3: 'Reply on RC3', Xu Ning, 26 Jan 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4390/egusphere-2025-4390-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4390-AC3

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by Xu Ning on behalf of the Authors (28 Jan 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (29 Jan 2026) by Mohamed Salim

RR by Anonymous Referee #2 (08 Feb 2026)

RR by Anonymous Referee #1 (13 Feb 2026)

ED: Publish as is (15 Feb 2026) by Mohamed Salim

AR by Xu Ning on behalf of the Authors (24 Feb 2026) Manuscript

Journal article(s) based on this preprint

03 Mar 2026

Implementation of a sigma coordinate system in PALM-Sigma v1.0 (based on PALM v21.10) for LES study of the marine atmospheric boundary layer

Xu Ning and Mostafa Bakhoday-Paskyabi

Geosci. Model Dev., 19, 1769–1789, https://doi.org/10.5194/gmd-19-1769-2026,https://doi.org/10.5194/gmd-19-1769-2026, 2026

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Xu Ning and Mostafa Bakhoday-Paskyabi

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Ocean waves shape winds close to the surface and extend their impact throughout the atmospheric boundary layer. In this study, we built a new modeling tool that allows simulations to follow the moving wave surface itself. By testing different wave and wind conditions, we show how waves change air motion, turbulence, and energy exchange above the ocean. This approach improves our ability to represent air–sea interactions, with implications for weather studies and offshore wind energy.


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