Review article:&nbsp;The future of the physics-based NWP methodology: a critical review on applications of catastrophe theory to the atmospheric science

Liu, Chongjian; Yin, Jinfang; Wei, Xiaomin; Sun, Xiaogong; Zhu, Guofu

doi:10.5194/egusphere-2026-2981

Preprints

https://doi.org/10.5194/egusphere-2026-2981

Preprints

26 Jun 2026

| 26 Jun 2026

Review article: The future of the physics-based NWP methodology: a critical review on applications of catastrophe theory to the atmospheric science

Chongjian Liu, Jinfang Yin, Xiaomin Wei, Xiaogong Sun, and Guofu Zhu

Abstract. The physics-based NWP (Numerical Weather Prediction) methodology appears increasingly difficult to enhance the NWP model’s forecasting capabilities. This is caused largely by catastrophe/tipping phenomena in the atmosphere as well as the multiplicity of NWP equation solutions. Classical physics from Newtonian mechanics to Einstein’s general relativity is essentially the theory of various kinds of smooth behavior other than catastrophe phenomena (water suddenly boils, a cell doubles cancerously etc.) while catastrophe theory (CT) provides a methodology for mathematical treatment of continuous action producing a discontinuous result, and has broad application prospects in numerous subjects. Studies of catastrophe have never stopped but the closely related terminology (tipping) changed subtly, and thus similarities and differences between catastrophe and tipping as well as the rhetoric course of change and development with tipping points have been ascertained in this article with the result showing that CT itself never declines and it gets a new replacer only. Both problems of the NWP development bottleneck and the highly acclaimed AI-weather models enslaved to its knowledge quality could be basically attributed to the emergence of catastrophic/tipping points owing to the nonlinearity of model equations. In this Critical Review, via a comprehensive review and the relevant analyses, we are led to the conclusion that it would be sagacious to first determine which one is the “physical solution” and/or incorporate (e.g.) the second law of thermodynamics as an additional constraint into the NWP model so as to reduce the number of solutions.

Received: 24 May 2026 – Discussion started: 26 Jun 2026

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Chongjian Liu, Jinfang Yin, Xiaomin Wei, Xiaogong Sun, and Guofu Zhu

Status: final response (author comments only)

CC1:
'Comment on egusphere-2026-2981', Nima Zafarmomen, 04 Jul 2026
The manuscript provides a broad and interesting review of catastrophe theory and its possible relevance to physics-based numerical weather prediction. The topic is timely and potentially valuable, but the manuscript would benefit from several minor revisions to improve clarity, structure, and balance.
The manuscript discusses catastrophe theory, tipping points, NWP limitations, AI-weather models, and thermodynamic constraints. The authors should state more clearly whether the main aim is to provide a literature review, a conceptual critique of current NWP, or a proposal for a future NWP methodology.

Terms such as “catastrophe,” “tipping point,” “bifurcation,” “multiple equilibria,” “multiple solutions,” and “physical solution” are central to the argument. A short definition table or concise explanatory paragraph would help readers from outside nonlinear dynamics.

Several sentences are long and difficult to follow. Careful language editing is recommended to improve grammar, sentence structure, and overall readability.

The argument that physics-based NWP may be approaching a development limit is interesting, but some statements are quite strong. The authors should either provide stronger quantitative support or present these points more cautiously as hypotheses.

Since Figure 1 is used to support the claim that forecast-score improvement is slowing, the authors should explain more clearly how the metrics were selected, how they should be compared, and what limitations exist in drawing this conclusion from the figure.

The review summarizes many catastrophe-theory applications, but the practical pathway for using catastrophe theory in NWP remains unclear. The authors should briefly explain how CT could inform model development, data assimilation, ensemble forecasting, or forecast interpretation.

The authors are strongly recommended to cite recent work on the use of large language models for adverse weather reasoning. In particular, Zafarmomen, N. and Samadi, V.: Can large language models effectively reason about adverse weather conditions?, Environmental Modelling & Software, 188, 106421, 2025, directly addresses whether LLMs can effectively reason about adverse weather conditions using U.S. National Weather Service flood-report data and several transformer-based models, including BART, BERT, LLaMA-2, LLaMA-3, and LLaMA-3.1. This reference is highly relevant to the manuscript’s discussion of AI-weather models and would strengthen the coverage of recent AI/LLM applications in weather and hazard-related contexts.
Citation: https://doi.org/10.5194/egusphere-2026-2981-CC1
- AC1: 'Reply on CC1', Chongjian Liu, 07 Jul 2026
  
  Please see the supplement file for further details.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2981-AC1
RC1:
'Comment on egusphere-2026-2981', Anonymous Referee #1, 29 Jul 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2981/egusphere-2026-2981-RC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2026-2981-RC1
- AC2: 'Reply on RC1', Chongjian Liu, 04 Aug 2026
  
  Please see the supplement (PDF). Thank you!
  
  Citation: https://doi.org/10.5194/egusphere-2026-2981-AC2
RC2: 'Comment on egusphere-2026-2981', Anonymous Referee #2, 14 Oct 2026

Thank you for inviting me to review paper: “Review article: The future of the physics-based NWP methodology: a crucial review on applications of catastrophe theory to the atmospheric science.”
This is one of the most difficult papers I have had to review, as I’m not sure some of the claims are justified. At the same time, the manuscript may contain profound suggestions worthy of detailed assessment by future researchers. In many places, I could not fully understand the key points. In that context, the best I can do is set out my interpretation of the paper below, in three main bullet points. These notes can then be used by the authors to help get their ideas across more clearly.
(1) As I understand it, catastrophe theory was a major new idea in the 1980s, when researchers began investigating nonlinear ordinary differential equations. In essence, the idea is that a forcing could change by only a small amount and, in some cases, cause a jump to another state. Furthermore, there could be hysteresis, so reversing the forcing parameter does not cause a return to the same state. Now, in 2026, almost everyone is aware of climate change and the risk of climate “tipping points”. Mathematically, tipping points are expressed through changes to bifurcation parameters, which are in turn related to summary features of climate change (e.g. global warming). Can the authors confirm, or explain any differences, between catastrophe theory and the more modern concept of tipping points? And what specific bits they believe are missing in current NWP models?
(2) I really want to better understand the main idea proposed by the authors, namely that step-change features in the climate system are not captured in weather forecast models (and, by association, climate models). It is true that much of the atmosphere and ocean system is governed by smooth fluids, so standard NWP discretisation is appropriate. But there are many “on-off” components that are treated rigorously in NWP/GCMs. For instance, phase changes that enable rainfall from vapour, the simulation of dynamic ice cover and its interactions with local climate. As many NWPs have been converted into Earth System Models (ESMs), they introduce even more nonlinear switches. For instance, the global carbon cycle and vegetation components correctly simulate edges between biome types, as seen in data such as EO retrievals. The authors may need to explain more precisely where they believe NWP deficiencies lie. What are the specific quantities, forcings and circumstances in which “hard-wiring” local tipping is expected to enhance forecasts?

(3) There remain some concerns in NWP. Although weather forecasts now operate at very high spatial resolutions, it remains necessary to parameterise even finer-resolution processes. Some of these processes are strongly nonlinear (convection, cloud formation, rainfall phase changes). Spatial averaging probably smooths out “switching” (i.e. localised catastrophic effects), so some standard discretisation is likely valid. Hence, I could imagine that some nonlinearity that is present in the real system becomes overlooked. This suggestion feels like the nearest I can think of to where the authors believe NWP is unable to capture strong nonlinearity? If this is the case, then there is a lot of literature in the meteorological journals that could be cited – and the authors need to more clearly state this?
I do want to be helpful, and I would be happy to see another version of the manuscript if NPG gives the authors permission to resubmit. There is always a concern that a paper that is radically different from the norm is not accepted because reviewers do not fully understand it. I do not want to be that reviewer, so I think we should give the authors a second opportunity with this manuscript.
More Minor Things:
The authors have targeted an English-language journal. I am sorry to say that the paper needs major improvement in its writing style. In many places, the word choice is inappropriate, likely selected with very good intentions from a thesaurus, but the context is very wrong. AI should never be used to generate text that is copied, but it is broadly acceptable to run parts of a paper through a grammar checker such as Grammarly. I think that software can also check context.
The figures need work to improve their presentation to meet the standards for a peer-reviewed journal. For instance, Figure 1 uses a mixture of font sizes, ranging from very large to extremely small. The tick labels are so small that, when I started this review from a paper copy, I simply could not read the numbers. Similarly, the axis labels are impossible to read. Standard format should have the unnecessary horizontal and vertical lines removed.
The paper feels long and very “text-heavy”. The authors might consider reducing the word count.

Citation: https://doi.org/10.5194/egusphere-2026-2981-RC2
EC1: 'Comment on egusphere-2026-2981', Olivier Talagrand, 19 Oct 2026

See attached file

Citation: https://doi.org/10.5194/egusphere-2026-2981-EC1

Chongjian Liu, Jinfang Yin, Xiaomin Wei, Xiaogong Sun, and Guofu Zhu

Viewed

Total article views: 493 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	BibTeX	EndNote
374	87	32	493	57	49

HTML: 374
PDF: 87
XML: 32
Total: 493
BibTeX: 57
EndNote: 49

Views and downloads (calculated since 26 Jun 2026)

Month	HTML	PDF	XML	Total
Jul 2026	65	23	5	93
Aug 2026	53	14	2	69
Sep 2026	132	18	12	162
Oct 2026	124	32	13	169

Cumulative views and downloads (calculated since 26 Jun 2026)

Month	HTML	PDF	XML	Total
Jul 2026	65	23	5	93
Aug 2026	53	14	2	69
Sep 2026	132	18	12	162
Oct 2026	124	32	13	169

Viewed (geographical distribution)

Total article views: 451 (including HTML, PDF, and XML) Thereof 451 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 30 Oct 2026

Short summary

The numerical weather prediction (NWP) is facing the challenge of development bottleneck, and this article, via a comprehensive review on application of catastrophe theory to the atmospheric science for revealing the fundamental logic why the physics-based NWP methodology would be about to approach its end with some remedial measures suggested for avoiding its finality to occur, might be helpful to promote the enhancement of NWP forecasting accuracy so as to break its development bottleneck.


Total:	0
HTML:	0
PDF:	0
XML:	0