the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Jul 2025
Stripe Patterns in Wind Forecasts Induced by Physics-Dynamics Coupling on a Staggered Grid in CMA-GFS 3.0
Abstract. An unphysical stripe pattern is identified in low-level wind field in China Meteorological Administration Global Forecast System (CMA-GFS), characterized by meridional stripes in u-component and zonal stripes in v-component. This stripe noise is primarily confined to the planetary boundary layer over land. The absence of noise in both surface static fields and pure dynamic-core solutions proves that neither the dynamical core nor physical parameterizations alone can produce wind stripe patterns. These results suggest that staggered-grid mismatch in physics-dynamics coupling is likely the primary mechanism. Idealized two-dimensional experiments demonstrate that combining one-dimensional dynamic-core advection and physics-based vertical diffusion on a staggered grid generates 2Δx-wavelength spurious waves when surface friction is non-uniform. One-dimensional linear wave analysis further confirms that staggered-grid coupling between dynamic advection and inhomogeneous damping forcing induces dispersion errors in wave solutions. Sensitivity tests validate that eliminating grid mismatch in physics-dynamic coupling removes this stripe noise. These findings collectively indicate that while staggered grids benefit the dynamic core’s numerical stability and accuracy, their inherent grid mismatch with physics parameterizations requires specialized coupling strategies to avoid spurious noise. Potential solutions to remedy this issue are discussed.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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CEC1: 'Comment on egusphere-2025-2704 - No compliance with the policy of the journal', Juan Antonio Añel, 25 Jul 2025
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AC1: 'Reply on CEC1', Jiong Chen, 26 Jul 2025
Dear Dr. Añel,
Thank you for your guidance regarding the code submission. We have uploaded the CMA-GFS 3.0 model code and the code decription to Baidu Cloud (link: https://pan.baidu.com/s/1FYy6u7X5auH2P2Hju6ncnA). The access password has been securely shared with the GMD editorial office and Dr. Caldwell, who will forward it to you and the reviewers.
We appreciate your understanding of these access arrangements and remain fully committed to meeting GMD's transparency standards. Please don't hesitate to contact us if you encounter any issues accessing the materials.
Best regards,
Jiong ChenCitation: https://doi.org/10.5194/egusphere-2025-2704-AC1 -
CEC2: 'Reply on AC1', Juan Antonio Añel, 27 Jul 2025
Dear authors,
Unfortunately, your reply does not solve the situation. First, we can not accept Baidu.com for you deposit of the code. You must deposit it in one of the acceptable repositories listed in our policy. This is clearly stated there, in the link that I included in my previous email. I would ask you to read and pay close attention to it.
Also, beyond the issue with the repository, to restrict the availability of the code only to the Editors and reviewers, you need to handle us evidence that you are not allowed to share the code with the general public. Again, this means that you need to handle us documentary evidence of it: for example, a license, a law, an order signed by an authority.
As I mentioned in my previous comment, if you do not address the mentioned issues, we can not publish your manuscript in our journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-2704-CEC2 -
AC2: 'Reply on CEC2', Jiong Chen, 28 Jul 2025
Dear Dr. Añel,
We have now received approval to publicly release the CMA-GFS 3.0 model code related to our manuscript "Stripe Patterns in Wind Forecasts Induced by Physics-Dynamics Coupling on a Staggered Grid in CMA-GFS 3.0" (ID: egusphere-2025-2704).
The complete code package with a description has been deposited on Zenodo:
https://doi.org/10.5281/zenodo.16516966Please let us know if you encounter any issues accessing the code. We appreciate your guidance throughout this process.
Best regards,
Jiong Chen
Citation: https://doi.org/10.5194/egusphere-2025-2704-AC2 -
CEC3: 'Reply on AC2', Juan Antonio Añel, 28 Jul 2025
Dear authors,
Many thanks for addressing this issue so quickly, and for your work towards sharing the code of the model. We can consider now the current version of your manuscript in compliance with the Code and Data policy of the journal. Please, do not forget to update the "Code and Data Availability" section with the information for the repository containing the code in any reviewed version of your manuscript.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-2704-CEC3 -
AC3: 'Reply on CEC3', Jiong Chen, 29 Jul 2025
Dear Dr. Añel,
Thank you for your prompt confirmation and for your guidance throughout the code sharing process. We appreciate the journal's commitment to research transparency. We confirm that the "Code and Data Availability" section will be updated in all future reviewed versions of the manuscript.
Best regards,
Jiong Chen
Citation: https://doi.org/10.5194/egusphere-2025-2704-AC3
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AC3: 'Reply on CEC3', Jiong Chen, 29 Jul 2025
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CEC3: 'Reply on AC2', Juan Antonio Añel, 28 Jul 2025
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AC2: 'Reply on CEC2', Jiong Chen, 28 Jul 2025
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CEC2: 'Reply on AC1', Juan Antonio Añel, 27 Jul 2025
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AC1: 'Reply on CEC1', Jiong Chen, 26 Jul 2025
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RC1: 'Comment on egusphere-2025-2704', Nigel Wood, 30 Jul 2025
Stripe Patterns in Wind Forecasts Induced by Physics-Dynamics Coupling on a Staggered Grid in CMA-GFS 3.0 by Jiong Chen, Yong Su, Zhe Li, Zhanshan Ma and Xueshun Shen
[Some maths characters have been lost in the cut-n-pasting from my original document - to see the full content please see the attached PDF]
This is a very interesting investigation into the cause of, and aspects of a remedy for, the appearance of stripes in wind forecasts. The authors:
- present the problem clearly,
- discuss the possible cause,
- present the results of an idealised model to support their hypothesis,
- develop a theoretical model to show what is going on,
- and then show the positive impact of one approach to avoiding the problem.
This is a great example of the scientific method at work and the results are all clearly presented.
I have only one comment that I have listed as a main point which is a suggestion for how I think the authors could give some more insight into what is going on and that would add some value to the presentation.
Other than that, I am happy to recommend publication subject to various rather minor comments/questions/suggestions listed below. The length of some of these might suggest a more major nature but my intention is that of Minor Revision.
Main point
The one aspect of the presentation that I think could be improved is for the authors to give the reader better clarity on what is going on and how it leads to the results seen.
In terms of the analysis section 3.4 there are two models of the damping process:
[PLEASE SEE ATTACHED PDF!]
and
[PLEASE SEE ATTACHED PDF!]
There are two steps that lead to noise being induced by process B.
The first step is common to both A and B. It is perhaps clear to many readers but I think it would be worth being explicit that applying either A or B to even (or perhaps especially) an initially constant field will induce a variation in that field that reflects the variation of . Such an effect is clear from the results of the control experiment in Fig 7e where the initially uniform wind is damped to zero at one point but remains almost at its initial value upstream of that point – the horizontal variation of is reflected in the wind field.
The next step in the argument is that for process B, the combination of horizontal variation in and averaging of fields back and forth leads to a dispersive error in how the wind field evolves that is not seen for process A (for which the impact of the damping coefficient is purely local). That this is the case can be seen by rewriting process B as:
[PLEASE SEE ATTACHED PDF!]
In this form two things become apparent:
- The first term is perhaps not surprising. It has the form of a second-order accurate horizontal diffusion scheme. Any mode, that emerges by whatever route, is invisible to this term and so will not be damped at all. Other modes will also be impacted by the smoothing inherent in the 1-2-1 operator. (In contrast, process A will damp all modes equally as efficiently.)
- More interestingly perhaps, the second term can be interpreted as a second-order centred-difference advection scheme where the advecting “velocity” is . This term is therefore not damping at all. It is also the source of the dispersion issue: When applied to a field with a discontinuous field such a scheme is well known to create upstream propagating noise. Indeed, Fig 3.7a of Durran’s second edition of Numerical Methods for Fluid Dynamics is very reminiscent of the form of the result of process B shown in Fig 7e of the present work.
None of this says a lot more than the authors already present in their work but I feel that adding a brief discussion of the form (C) and making the analogy with centred advection (and its dispersion error and associated noise) might, for some readers, give a bit more insight into what is happening.
Minor comments
(Lnn refers to line number nn.)
- L13: I am not convinced that the comment about the absence of noise in the static fields is quite correct – see my comment below about L177. I would suggest instead saying something like ‘the structure of the static fields in not consistent with the amplitude of the noise if that noise were forced locally by the static fields’?
- L80-83: The UK Met Office model does not follow this approach. It averages the winds to the cell centre but only uses these averaged winds to evaluate the boundary layer diffusion coefficient (the eddy diffusivity). It then averages the diffusion coefficient back to the wind points and performs the vertical diffusion at the wind points. This is the approach that I would recommend in solving the problem presented in this paper if your infrastructure can support such an approach.
- L156-157: It would be good somewhere to comment on the stability of the model, i.e. is the amplitude of the stripes approximately constant in that they appear and remain approximately unchanged, or do they grow in time?
- L177: Without further evidence to support this, I think ‘complete absence’ is too strong. It is clear that there is not the same visual level of noise at the scale as in Fig 2 but that is not the same as there being a complete absence. And given that horizontal averaging of a field cannot create a component then I think that the heart of the later argument lies in there being some forcing of such a component by the physics. It would be interesting to present a spectral analysis of these fields in the same way as Fig 9.
- L182: It would be useful to the reader to give an indicative latitude and longitude for where the islands are.
- L209, section 3.3: I think here one is looking for the simplest experimental set-up that shows the noisy behaviour. Given the theoretical model used in section 3.4 I would have thought that it would be best in this section to match as closely as possible that theoretical model, i.e. use a constant advecting wind (thereby losing the complication of nonlinearity) and use a constant eddy viscosity in the vertical (thereby losing the complication of nonzero values of . If the hypothesis is correct then the equivalent figures to Figs 7a, b and e should be very similar.
- L216: If the authors do retain a height varying then it is probably worth saying that this is an example profile for the purposes of the idealised model rather than the profile used in the full model.
- Equation (5): I believe there is a missing factor of .
- L220/236: To save the reader having to work it out for themselves, it would be good to state that the time step is 300s (if I have worked it out correctly!).
- L241: It would be useful to say whether the noise grows or is stable.
- L252, Fig 7: It would be worth stating in the caption that ‘x-grid’ means the grid point number not a distance.
- L255-256: I am not convinced that the words used for either source of ‘noise’ are correct. Earlier it has been stated that there is a complete absence of noise in the surface fields of the full model! The surface forcing is what it is – it is the amplification, or exposure (through dispersion), of whatever component that is at question. Also, I think it is debatable whether that averaging is an inconsistency; I would suggest that it is a discretization choice (albeit perhaps not a good choice!).
- L272 and following lines: The authors have included one part of the averaging process, from the physics points (cell centres) to the velocity points (cell faces). They have then used Taylor series expansions to estimate the winds at the cell centres. It would be better (and no more difficult) to explicitly include the averaging of the winds to the cell centres and then use Taylor series expansions to obtain estimates for in terms of . This has the effect of changing, in Eq. (10), the denominator 8 to 4, and the denominator 48 to 12. Although this is only a minor change in practice, it better reflects what the model of section 3.3 actually does, and perhaps more usefully, the terms that are proportional to are proportional to which are the terms that arise in a second-order centred advection scheme (as expected from the analysis suggested in the section Main Point).
- L275: Strictly, Eq. (10) is only the solution to Eq. (8) if and are taken as independent of which they cannot both be over a periodic domain. You could either rewrite (8) in terms of and and then postulate a different problem that has those coefficients constant, or simply say that the solution is approximate and only holds locally.
- L277: Related to the above point, I think here (and everywhere they are used) and should be written as and to make their horizontal dependency clear.
- L277: It would be much better to not include the factor of 1/2 in the definition of but carry that explicitly where is used. Otherwise the definition is not consistent with the use of elsewhere, e.g., consider what happens if , we would then end up with !
- L280: It would be worth reminding the reader somewhere that the Taylor series expansion is only valid for small values of . Otherwise, when , as it can do, the solution (both (10) and (11)) would be predicted to grow unlimitedly since .
- L303: The approach of this section makes sense and is a nice way of showing that the noise can be controlled. However, it is perhaps worth pointing out that the approach used to do so introduces an arbitrary bias in the direction in which the now piecewise-constant sampling is done, i.e. why choose instead of ? I appreciate that this would not be practicable as a quick experiment, but a better approach might be to always sample upwind, e.g., when and
- L310: Please say whether this is also applied for the reverse mapping from the physics point back to the dynamics point.
- L342: I feel that there is still an interesting level of difference in the spectra over the sea, more than ‘remarkable consistency’ would suggest.
- L401-409: It is a shame if it is not possible within CMA-GFS to apply the boundary-layer code to wind fields on their native points. This would seem to me to be the preferred solution rather than reintroducing horizontal diffusion. And, as I noted earlier, this is the approach taken within the Met Office’s Unified Model.
Typos/editorial comments
- L13: ‘dynamical core’ is more standard than ‘dynamic-core’
- L21: ‘physics-dynamics’ is more standard than ‘physics-dynamic’
- L130: word missing from ‘therefore systematically these’
- L243: ‘Compared’ should be ‘Comparing’
- L280: There is an overbar missing from the
- L284: The exponent in the middle term, together with the factor , need to be removed
Nigel Wood
July 2025
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AC4: 'Reply on RC1', Jiong Chen, 20 Aug 2025
Dear Dr. Wood,
We sincerely appreciate your thorough evaluation and constructive suggestions for our manuscript "Stripe Patterns in Wind Forecasts Induced by Physics-Dynamic Coupling on a Staggered Grid in CMA-GFS 3.0". Your insightful comments not only affirm the value of this work but have also significantly helped us refine both the technical rigor and clarity of presentation. In particular, your detailed description of the UK Met Office model's solution to this issue has provided invaluable inspiration, guiding our next steps in adapting and implementing similar improvements in CMA-GFS.
In the attached file, we respond point-by-point to your comments, outlining how we plan to address them in the revised manuscript pending all reviewer feedback. All of our replies are presented in bold Calibri font. Any wording that will be incorporated directly into the revised manuscript is set in Times New Roman in the following paragraph.
Best regards
Jiong Chen
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AC5: 'Reply on AC4', Jiong Chen, 20 Aug 2025
A revision is required for the phase velocity in Eq. (12). It should be
c' = c^D + (∆α_j ∆x)/4 - (k² ∆α_j ∆x³)/24
rather than
c' = c^D + (k ∆α_j ∆x)/4 + (k³ ∆α_j ∆x³)/24.Citation: https://doi.org/10.5194/egusphere-2025-2704-AC5 -
RC2: 'Reply on AC4', Nigel Wood, 20 Aug 2025
My thanks to the authors for their careful and considered responses to my comments and suggestions.
In the spirit of interactive discussion, I thought it worth pointing out what I think is an error: in your reply to my minor comment 17 it is stated that "this doesn't affect our analysis of 2Δx waves (kΔx = π/2)". Apart from the fact that π/2>1 (and hence the Taylor series expansion is invalid), the wavelength of 2Δx waves is λ=2Δx and hence the wavenumber is k≡2π/λ=2π/(2Δx) = π/Δx. Therefore, kΔx=π (see also, e.g., p102 between equations (3.31) and (3.32) of Durran's book, second edition). The truncation analysis is not valid for this wave (or others close to the resolvable limit), it is only valid for the longer, well resolved waves i.e. for kΔx<<1.
If you did want an analysis that is valid also for the shorter waves then I would suggest, instead of using a Taylor series analysis for the spatial variation, you instead seek solutions ∝ exp(ikx) and gather terms together to give solutions in sin(kΔx) and cos(kΔx). [Indeed, you already do seek a solution of this form but only after you have already made the Taylor expansion - you would retain more information about the system by doing it before (or instead of) making the Taylor expansion. If you want to identify the leading order terms then you can always expand the sin(kΔx) and cos(kΔx) terms as powers of kΔx for the case when kΔx<<1. But this way you retain information also about how the shorter waves behave.]
Nigel
Citation: https://doi.org/10.5194/egusphere-2025-2704-RC2 -
AC6: 'Reply on RC2', Jiong Chen, 22 Aug 2025
Dear Nigel,
Thank you very much for catching this!
You are absolutely right about the wavenumber – that was a slip-up on our part in the response, and we appreciate you pointing it out so clearly. The wavelength λ for a 2Δx wave should indeed be 2π, not π. Therefore the wavenumber is defined as k ≡ 2π/λ, which gives k = 2π/(2Δx) = π/Δx. Consequently, kΔx = π.
For this 2Δx wave, the Taylor expansion around kΔx = π is not valid. The higher-order terms (e.g., the 4th-order term) are not negligible at this point because ξ = π - kΔx is not a small parameter here. Therefore, performing a Taylor expansion and truncating it is not suitable for analyzing the short-wave (kΔx → π) limit.
I made a second mistake by confusing the object of our analysis. Although this study aims to diagnose the cause of 2Δx waves, our focus regarding the numerical solution from Eq. (6) is on the long-wave and well-resolved components of the variable u, not on the 2Δx waves themselves. The 2Δx oscillations are spurious, artificial modes that we need to find ways to eliminate or control.
Therefore, for the purpose of this study—accurately understanding the behavior of the physical, resolvable scales—the Taylor expansion is indeed valid and appropriate for analyzing the long-wave limit.
Based on the above considerations, we revise the original sentence from:
"For numerically resolved scales (|k∆x|≤π⁄2) where Taylor expansions remain valid, the variable u at neighboring grid points can be approximated as:"
to:
"For numerically resolved scales (k∆x<<1) where Taylor expansions remain valid, the variable u at neighboring grid points can be approximated as:"
Here, we have only modified the criterion formula, but our understanding is completely different.
In accordance with your recommendations, a Von Neumann stability analysis has been conducted to examine the amplification factor. The results corroborate the initial conclusion, demonstrating that the coupling of inhomogeneous physical forcing with a staggered-grid discretization scheme acts as a source of numerical dispersion. Please refer to the attached PDF for the specific analytical details.
Of course, the Von Neumann method can be further extended by applying Taylor expansions to the sine and cosine functions to analyze the dissipation and dispersion characteristics for both long-wave and short-wave limits. However, for the specific problem addressed in this study, our original analysis remains valid and sufficient. Therefore, we will retain the original approach in the manuscript.
Jiong
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AC6: 'Reply on RC2', Jiong Chen, 22 Aug 2025
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AC5: 'Reply on AC4', Jiong Chen, 20 Aug 2025
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RC3: 'Comment on egusphere-2025-2704', Sean Santos, 26 Sep 2025
This manuscript is an intriguing analysis of how physics-dynamics coupling can lead to numerical artifacts (striping) when the physics and dynamical processes are evaluated using data non-collocated grid points. It combines, in my view successfully, results from global model experiments, a simplified numerical model demonstrating similar difficulties, and a theoretical analysis of how staggered winds may lead to dispersive behavior. The presentation of most points is clear and convincing, and most of my concerns with the originally submitted draft have already been corrected in the response to Nigel Wood.
I have two minor concerns outstanding. First, the equation (7) in the manuscript is not the analytic solution to (6) if α is spatially varying. An example is given in the attachment. The effect of the spatially-varying α is simply to modulate the amplitude of the wave through inhomogeneous damping, so I do not think this causes problems for the paper's main argument. I think it would be fine to omit the analytic solution in (7) entirely, since the important point in this section is that using half-grid-scale offsets introduces extra dispersion not present in other discretizations.
The other minor issue is the use of the word "discontinuous'' on line 299 of the original paper. From this paper, I don't see that you necessarily need surface friction to be discontinuous at some particular point to produce these numerical artifacts; rather, surface friction only needs significant variability at the grid scale.
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AC7: 'Reply on RC3', Jiong Chen, 30 Sep 2025
Dear Dr. Santos,
Thank you very much for your thoughtful review and for your encouraging comments on our manuscript.
Regarding your two specific comments:
Comment on Equation (7):
You are absolutely correct that Equation (7) is not an exact analytical solution to Equation (6) when α varies spatially. Following Dr. Wood’s comments, our revised discussion now focuses on the discrete solution of Equation (6). Therefore, we will remove the original analytical solution (Equation 7) and its related discussion from the manuscript.Comment on the term “discontinuous” (Line 299):
We thank you for this meticulous observation. You are right that the presence of numerical artifacts does not require surface friction to be strictly discontinuous, but only to exhibit significant grid-scale variability. Accordingly, we will replace the word “discontinuous” with “non-uniform”.Once again, we deeply appreciate your time and valuable suggestions, which will help us enhance the clarity and rigor of our paper.
Jiong Chen
Citation: https://doi.org/10.5194/egusphere-2025-2704-AC7
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AC7: 'Reply on RC3', Jiong Chen, 30 Sep 2025
Interactive discussion
Status: closed
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CEC1: 'Comment on egusphere-2025-2704 - No compliance with the policy of the journal', Juan Antonio Añel, 25 Jul 2025
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.htmlI need to be very clear here, we can not accept that you do not share the code of the CMA-GFS 3.0. Actually, given the claim that you make in the Code and Data Availability section of your mansucript, it should have not been accepted for Discussions. Therefore, the situation with your manuscript is highly irregular.
Therefore, you must respond to this comment with a link and permanent handler (e.g. DOI) for an acceptable repository (see our policy for options) containing the code of the CMA-GFS 3.0. If you are forbidden to share it because of a legal reason, then you continue to have the obligation to reply with a private repository containing the code, and make it accessible to the Topical Editor and I, and the reviewers. Please, do it in a prompt manner.
I must note that if you do not fix this problem, we can not continue with the peer-review process or accept your manuscript in our journal.
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2025-2704-CEC1 -
AC1: 'Reply on CEC1', Jiong Chen, 26 Jul 2025
Dear Dr. Añel,
Thank you for your guidance regarding the code submission. We have uploaded the CMA-GFS 3.0 model code and the code decription to Baidu Cloud (link: https://pan.baidu.com/s/1FYy6u7X5auH2P2Hju6ncnA). The access password has been securely shared with the GMD editorial office and Dr. Caldwell, who will forward it to you and the reviewers.
We appreciate your understanding of these access arrangements and remain fully committed to meeting GMD's transparency standards. Please don't hesitate to contact us if you encounter any issues accessing the materials.
Best regards,
Jiong ChenCitation: https://doi.org/10.5194/egusphere-2025-2704-AC1 -
CEC2: 'Reply on AC1', Juan Antonio Añel, 27 Jul 2025
Dear authors,
Unfortunately, your reply does not solve the situation. First, we can not accept Baidu.com for you deposit of the code. You must deposit it in one of the acceptable repositories listed in our policy. This is clearly stated there, in the link that I included in my previous email. I would ask you to read and pay close attention to it.
Also, beyond the issue with the repository, to restrict the availability of the code only to the Editors and reviewers, you need to handle us evidence that you are not allowed to share the code with the general public. Again, this means that you need to handle us documentary evidence of it: for example, a license, a law, an order signed by an authority.
As I mentioned in my previous comment, if you do not address the mentioned issues, we can not publish your manuscript in our journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-2704-CEC2 -
AC2: 'Reply on CEC2', Jiong Chen, 28 Jul 2025
Dear Dr. Añel,
We have now received approval to publicly release the CMA-GFS 3.0 model code related to our manuscript "Stripe Patterns in Wind Forecasts Induced by Physics-Dynamics Coupling on a Staggered Grid in CMA-GFS 3.0" (ID: egusphere-2025-2704).
The complete code package with a description has been deposited on Zenodo:
https://doi.org/10.5281/zenodo.16516966Please let us know if you encounter any issues accessing the code. We appreciate your guidance throughout this process.
Best regards,
Jiong Chen
Citation: https://doi.org/10.5194/egusphere-2025-2704-AC2 -
CEC3: 'Reply on AC2', Juan Antonio Añel, 28 Jul 2025
Dear authors,
Many thanks for addressing this issue so quickly, and for your work towards sharing the code of the model. We can consider now the current version of your manuscript in compliance with the Code and Data policy of the journal. Please, do not forget to update the "Code and Data Availability" section with the information for the repository containing the code in any reviewed version of your manuscript.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-2704-CEC3 -
AC3: 'Reply on CEC3', Jiong Chen, 29 Jul 2025
Dear Dr. Añel,
Thank you for your prompt confirmation and for your guidance throughout the code sharing process. We appreciate the journal's commitment to research transparency. We confirm that the "Code and Data Availability" section will be updated in all future reviewed versions of the manuscript.
Best regards,
Jiong Chen
Citation: https://doi.org/10.5194/egusphere-2025-2704-AC3
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AC3: 'Reply on CEC3', Jiong Chen, 29 Jul 2025
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CEC3: 'Reply on AC2', Juan Antonio Añel, 28 Jul 2025
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AC2: 'Reply on CEC2', Jiong Chen, 28 Jul 2025
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CEC2: 'Reply on AC1', Juan Antonio Añel, 27 Jul 2025
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AC1: 'Reply on CEC1', Jiong Chen, 26 Jul 2025
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RC1: 'Comment on egusphere-2025-2704', Nigel Wood, 30 Jul 2025
Stripe Patterns in Wind Forecasts Induced by Physics-Dynamics Coupling on a Staggered Grid in CMA-GFS 3.0 by Jiong Chen, Yong Su, Zhe Li, Zhanshan Ma and Xueshun Shen
[Some maths characters have been lost in the cut-n-pasting from my original document - to see the full content please see the attached PDF]
This is a very interesting investigation into the cause of, and aspects of a remedy for, the appearance of stripes in wind forecasts. The authors:
- present the problem clearly,
- discuss the possible cause,
- present the results of an idealised model to support their hypothesis,
- develop a theoretical model to show what is going on,
- and then show the positive impact of one approach to avoiding the problem.
This is a great example of the scientific method at work and the results are all clearly presented.
I have only one comment that I have listed as a main point which is a suggestion for how I think the authors could give some more insight into what is going on and that would add some value to the presentation.
Other than that, I am happy to recommend publication subject to various rather minor comments/questions/suggestions listed below. The length of some of these might suggest a more major nature but my intention is that of Minor Revision.
Main point
The one aspect of the presentation that I think could be improved is for the authors to give the reader better clarity on what is going on and how it leads to the results seen.
In terms of the analysis section 3.4 there are two models of the damping process:
[PLEASE SEE ATTACHED PDF!]
and
[PLEASE SEE ATTACHED PDF!]
There are two steps that lead to noise being induced by process B.
The first step is common to both A and B. It is perhaps clear to many readers but I think it would be worth being explicit that applying either A or B to even (or perhaps especially) an initially constant field will induce a variation in that field that reflects the variation of . Such an effect is clear from the results of the control experiment in Fig 7e where the initially uniform wind is damped to zero at one point but remains almost at its initial value upstream of that point – the horizontal variation of is reflected in the wind field.
The next step in the argument is that for process B, the combination of horizontal variation in and averaging of fields back and forth leads to a dispersive error in how the wind field evolves that is not seen for process A (for which the impact of the damping coefficient is purely local). That this is the case can be seen by rewriting process B as:
[PLEASE SEE ATTACHED PDF!]
In this form two things become apparent:
- The first term is perhaps not surprising. It has the form of a second-order accurate horizontal diffusion scheme. Any mode, that emerges by whatever route, is invisible to this term and so will not be damped at all. Other modes will also be impacted by the smoothing inherent in the 1-2-1 operator. (In contrast, process A will damp all modes equally as efficiently.)
- More interestingly perhaps, the second term can be interpreted as a second-order centred-difference advection scheme where the advecting “velocity” is . This term is therefore not damping at all. It is also the source of the dispersion issue: When applied to a field with a discontinuous field such a scheme is well known to create upstream propagating noise. Indeed, Fig 3.7a of Durran’s second edition of Numerical Methods for Fluid Dynamics is very reminiscent of the form of the result of process B shown in Fig 7e of the present work.
None of this says a lot more than the authors already present in their work but I feel that adding a brief discussion of the form (C) and making the analogy with centred advection (and its dispersion error and associated noise) might, for some readers, give a bit more insight into what is happening.
Minor comments
(Lnn refers to line number nn.)
- L13: I am not convinced that the comment about the absence of noise in the static fields is quite correct – see my comment below about L177. I would suggest instead saying something like ‘the structure of the static fields in not consistent with the amplitude of the noise if that noise were forced locally by the static fields’?
- L80-83: The UK Met Office model does not follow this approach. It averages the winds to the cell centre but only uses these averaged winds to evaluate the boundary layer diffusion coefficient (the eddy diffusivity). It then averages the diffusion coefficient back to the wind points and performs the vertical diffusion at the wind points. This is the approach that I would recommend in solving the problem presented in this paper if your infrastructure can support such an approach.
- L156-157: It would be good somewhere to comment on the stability of the model, i.e. is the amplitude of the stripes approximately constant in that they appear and remain approximately unchanged, or do they grow in time?
- L177: Without further evidence to support this, I think ‘complete absence’ is too strong. It is clear that there is not the same visual level of noise at the scale as in Fig 2 but that is not the same as there being a complete absence. And given that horizontal averaging of a field cannot create a component then I think that the heart of the later argument lies in there being some forcing of such a component by the physics. It would be interesting to present a spectral analysis of these fields in the same way as Fig 9.
- L182: It would be useful to the reader to give an indicative latitude and longitude for where the islands are.
- L209, section 3.3: I think here one is looking for the simplest experimental set-up that shows the noisy behaviour. Given the theoretical model used in section 3.4 I would have thought that it would be best in this section to match as closely as possible that theoretical model, i.e. use a constant advecting wind (thereby losing the complication of nonlinearity) and use a constant eddy viscosity in the vertical (thereby losing the complication of nonzero values of . If the hypothesis is correct then the equivalent figures to Figs 7a, b and e should be very similar.
- L216: If the authors do retain a height varying then it is probably worth saying that this is an example profile for the purposes of the idealised model rather than the profile used in the full model.
- Equation (5): I believe there is a missing factor of .
- L220/236: To save the reader having to work it out for themselves, it would be good to state that the time step is 300s (if I have worked it out correctly!).
- L241: It would be useful to say whether the noise grows or is stable.
- L252, Fig 7: It would be worth stating in the caption that ‘x-grid’ means the grid point number not a distance.
- L255-256: I am not convinced that the words used for either source of ‘noise’ are correct. Earlier it has been stated that there is a complete absence of noise in the surface fields of the full model! The surface forcing is what it is – it is the amplification, or exposure (through dispersion), of whatever component that is at question. Also, I think it is debatable whether that averaging is an inconsistency; I would suggest that it is a discretization choice (albeit perhaps not a good choice!).
- L272 and following lines: The authors have included one part of the averaging process, from the physics points (cell centres) to the velocity points (cell faces). They have then used Taylor series expansions to estimate the winds at the cell centres. It would be better (and no more difficult) to explicitly include the averaging of the winds to the cell centres and then use Taylor series expansions to obtain estimates for in terms of . This has the effect of changing, in Eq. (10), the denominator 8 to 4, and the denominator 48 to 12. Although this is only a minor change in practice, it better reflects what the model of section 3.3 actually does, and perhaps more usefully, the terms that are proportional to are proportional to which are the terms that arise in a second-order centred advection scheme (as expected from the analysis suggested in the section Main Point).
- L275: Strictly, Eq. (10) is only the solution to Eq. (8) if and are taken as independent of which they cannot both be over a periodic domain. You could either rewrite (8) in terms of and and then postulate a different problem that has those coefficients constant, or simply say that the solution is approximate and only holds locally.
- L277: Related to the above point, I think here (and everywhere they are used) and should be written as and to make their horizontal dependency clear.
- L277: It would be much better to not include the factor of 1/2 in the definition of but carry that explicitly where is used. Otherwise the definition is not consistent with the use of elsewhere, e.g., consider what happens if , we would then end up with !
- L280: It would be worth reminding the reader somewhere that the Taylor series expansion is only valid for small values of . Otherwise, when , as it can do, the solution (both (10) and (11)) would be predicted to grow unlimitedly since .
- L303: The approach of this section makes sense and is a nice way of showing that the noise can be controlled. However, it is perhaps worth pointing out that the approach used to do so introduces an arbitrary bias in the direction in which the now piecewise-constant sampling is done, i.e. why choose instead of ? I appreciate that this would not be practicable as a quick experiment, but a better approach might be to always sample upwind, e.g., when and
- L310: Please say whether this is also applied for the reverse mapping from the physics point back to the dynamics point.
- L342: I feel that there is still an interesting level of difference in the spectra over the sea, more than ‘remarkable consistency’ would suggest.
- L401-409: It is a shame if it is not possible within CMA-GFS to apply the boundary-layer code to wind fields on their native points. This would seem to me to be the preferred solution rather than reintroducing horizontal diffusion. And, as I noted earlier, this is the approach taken within the Met Office’s Unified Model.
Typos/editorial comments
- L13: ‘dynamical core’ is more standard than ‘dynamic-core’
- L21: ‘physics-dynamics’ is more standard than ‘physics-dynamic’
- L130: word missing from ‘therefore systematically these’
- L243: ‘Compared’ should be ‘Comparing’
- L280: There is an overbar missing from the
- L284: The exponent in the middle term, together with the factor , need to be removed
Nigel Wood
July 2025
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AC4: 'Reply on RC1', Jiong Chen, 20 Aug 2025
Dear Dr. Wood,
We sincerely appreciate your thorough evaluation and constructive suggestions for our manuscript "Stripe Patterns in Wind Forecasts Induced by Physics-Dynamic Coupling on a Staggered Grid in CMA-GFS 3.0". Your insightful comments not only affirm the value of this work but have also significantly helped us refine both the technical rigor and clarity of presentation. In particular, your detailed description of the UK Met Office model's solution to this issue has provided invaluable inspiration, guiding our next steps in adapting and implementing similar improvements in CMA-GFS.
In the attached file, we respond point-by-point to your comments, outlining how we plan to address them in the revised manuscript pending all reviewer feedback. All of our replies are presented in bold Calibri font. Any wording that will be incorporated directly into the revised manuscript is set in Times New Roman in the following paragraph.
Best regards
Jiong Chen
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AC5: 'Reply on AC4', Jiong Chen, 20 Aug 2025
A revision is required for the phase velocity in Eq. (12). It should be
c' = c^D + (∆α_j ∆x)/4 - (k² ∆α_j ∆x³)/24
rather than
c' = c^D + (k ∆α_j ∆x)/4 + (k³ ∆α_j ∆x³)/24.Citation: https://doi.org/10.5194/egusphere-2025-2704-AC5 -
RC2: 'Reply on AC4', Nigel Wood, 20 Aug 2025
My thanks to the authors for their careful and considered responses to my comments and suggestions.
In the spirit of interactive discussion, I thought it worth pointing out what I think is an error: in your reply to my minor comment 17 it is stated that "this doesn't affect our analysis of 2Δx waves (kΔx = π/2)". Apart from the fact that π/2>1 (and hence the Taylor series expansion is invalid), the wavelength of 2Δx waves is λ=2Δx and hence the wavenumber is k≡2π/λ=2π/(2Δx) = π/Δx. Therefore, kΔx=π (see also, e.g., p102 between equations (3.31) and (3.32) of Durran's book, second edition). The truncation analysis is not valid for this wave (or others close to the resolvable limit), it is only valid for the longer, well resolved waves i.e. for kΔx<<1.
If you did want an analysis that is valid also for the shorter waves then I would suggest, instead of using a Taylor series analysis for the spatial variation, you instead seek solutions ∝ exp(ikx) and gather terms together to give solutions in sin(kΔx) and cos(kΔx). [Indeed, you already do seek a solution of this form but only after you have already made the Taylor expansion - you would retain more information about the system by doing it before (or instead of) making the Taylor expansion. If you want to identify the leading order terms then you can always expand the sin(kΔx) and cos(kΔx) terms as powers of kΔx for the case when kΔx<<1. But this way you retain information also about how the shorter waves behave.]
Nigel
Citation: https://doi.org/10.5194/egusphere-2025-2704-RC2 -
AC6: 'Reply on RC2', Jiong Chen, 22 Aug 2025
Dear Nigel,
Thank you very much for catching this!
You are absolutely right about the wavenumber – that was a slip-up on our part in the response, and we appreciate you pointing it out so clearly. The wavelength λ for a 2Δx wave should indeed be 2π, not π. Therefore the wavenumber is defined as k ≡ 2π/λ, which gives k = 2π/(2Δx) = π/Δx. Consequently, kΔx = π.
For this 2Δx wave, the Taylor expansion around kΔx = π is not valid. The higher-order terms (e.g., the 4th-order term) are not negligible at this point because ξ = π - kΔx is not a small parameter here. Therefore, performing a Taylor expansion and truncating it is not suitable for analyzing the short-wave (kΔx → π) limit.
I made a second mistake by confusing the object of our analysis. Although this study aims to diagnose the cause of 2Δx waves, our focus regarding the numerical solution from Eq. (6) is on the long-wave and well-resolved components of the variable u, not on the 2Δx waves themselves. The 2Δx oscillations are spurious, artificial modes that we need to find ways to eliminate or control.
Therefore, for the purpose of this study—accurately understanding the behavior of the physical, resolvable scales—the Taylor expansion is indeed valid and appropriate for analyzing the long-wave limit.
Based on the above considerations, we revise the original sentence from:
"For numerically resolved scales (|k∆x|≤π⁄2) where Taylor expansions remain valid, the variable u at neighboring grid points can be approximated as:"
to:
"For numerically resolved scales (k∆x<<1) where Taylor expansions remain valid, the variable u at neighboring grid points can be approximated as:"
Here, we have only modified the criterion formula, but our understanding is completely different.
In accordance with your recommendations, a Von Neumann stability analysis has been conducted to examine the amplification factor. The results corroborate the initial conclusion, demonstrating that the coupling of inhomogeneous physical forcing with a staggered-grid discretization scheme acts as a source of numerical dispersion. Please refer to the attached PDF for the specific analytical details.
Of course, the Von Neumann method can be further extended by applying Taylor expansions to the sine and cosine functions to analyze the dissipation and dispersion characteristics for both long-wave and short-wave limits. However, for the specific problem addressed in this study, our original analysis remains valid and sufficient. Therefore, we will retain the original approach in the manuscript.
Jiong
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AC6: 'Reply on RC2', Jiong Chen, 22 Aug 2025
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AC5: 'Reply on AC4', Jiong Chen, 20 Aug 2025
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RC3: 'Comment on egusphere-2025-2704', Sean Santos, 26 Sep 2025
This manuscript is an intriguing analysis of how physics-dynamics coupling can lead to numerical artifacts (striping) when the physics and dynamical processes are evaluated using data non-collocated grid points. It combines, in my view successfully, results from global model experiments, a simplified numerical model demonstrating similar difficulties, and a theoretical analysis of how staggered winds may lead to dispersive behavior. The presentation of most points is clear and convincing, and most of my concerns with the originally submitted draft have already been corrected in the response to Nigel Wood.
I have two minor concerns outstanding. First, the equation (7) in the manuscript is not the analytic solution to (6) if α is spatially varying. An example is given in the attachment. The effect of the spatially-varying α is simply to modulate the amplitude of the wave through inhomogeneous damping, so I do not think this causes problems for the paper's main argument. I think it would be fine to omit the analytic solution in (7) entirely, since the important point in this section is that using half-grid-scale offsets introduces extra dispersion not present in other discretizations.
The other minor issue is the use of the word "discontinuous'' on line 299 of the original paper. From this paper, I don't see that you necessarily need surface friction to be discontinuous at some particular point to produce these numerical artifacts; rather, surface friction only needs significant variability at the grid scale.
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AC7: 'Reply on RC3', Jiong Chen, 30 Sep 2025
Dear Dr. Santos,
Thank you very much for your thoughtful review and for your encouraging comments on our manuscript.
Regarding your two specific comments:
Comment on Equation (7):
You are absolutely correct that Equation (7) is not an exact analytical solution to Equation (6) when α varies spatially. Following Dr. Wood’s comments, our revised discussion now focuses on the discrete solution of Equation (6). Therefore, we will remove the original analytical solution (Equation 7) and its related discussion from the manuscript.Comment on the term “discontinuous” (Line 299):
We thank you for this meticulous observation. You are right that the presence of numerical artifacts does not require surface friction to be strictly discontinuous, but only to exhibit significant grid-scale variability. Accordingly, we will replace the word “discontinuous” with “non-uniform”.Once again, we deeply appreciate your time and valuable suggestions, which will help us enhance the clarity and rigor of our paper.
Jiong Chen
Citation: https://doi.org/10.5194/egusphere-2025-2704-AC7
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AC7: 'Reply on RC3', Jiong Chen, 30 Sep 2025
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
I need to be very clear here, we can not accept that you do not share the code of the CMA-GFS 3.0. Actually, given the claim that you make in the Code and Data Availability section of your mansucript, it should have not been accepted for Discussions. Therefore, the situation with your manuscript is highly irregular.
Therefore, you must respond to this comment with a link and permanent handler (e.g. DOI) for an acceptable repository (see our policy for options) containing the code of the CMA-GFS 3.0. If you are forbidden to share it because of a legal reason, then you continue to have the obligation to reply with a private repository containing the code, and make it accessible to the Topical Editor and I, and the reviewers. Please, do it in a prompt manner.
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Juan A. Añel
Geosci. Model Dev. Executive Editor