the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jun 2026
Emergence of chaos in the tropical atmosphere: Study of the weak temperature gradient system
Abstract. The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Nonlinear Processes in Geophysics.
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.- Preprint
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RC1: 'Comment on egusphere-2026-3631', Anonymous Referee #1, 25 Aug 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3631/egusphere-2026-3631-RC1-supplement.pdfReplyCitation: https://doi.org/
10.5194/egusphere-2026-3631-RC1 -
RC2: 'Comment on egusphere-2026-3631', Anonymous Referee #2, 18 Sep 2026
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The authors use a vorticity model to address the question of whether synoptic-scale tropical dynamics are chaotic or not, under the rather stringent assumptions of weak temperature gradient and time-independent wave-form divergence forcing. The model is then considered in a tropical strip domain with solid walls running parallel to the equator and Galerkin truncated based Fourier mode expansion. The results suggest that chaotic behaviour emerges under reasonably moderate forcing based on Lyapunov exponent analysis. The results are shown to be sensitive to a few key parameters such as the aspect ratio of the wave form, the meridional symmetry, and the amplitude of the forcing. As such, the work is quite original and interesting and deserves attention. However, the work is a bit too theoretical and does not make connections with the real tropical atmosphere; for instance, besides the divergence amplitude which is vaguely compared to values reported in literature, the choice of parameters is rarely justified by observations. It is, however, understandable as this is an exploratory paper and the authors promised to consider more realistic settings in the near future. The more serious shortcoming is the WTG approximation and the neglect of divergence modes that are known to dominate tropical dynamics and are strongly coupled with the Rossby modes. The most obvious example is the Madden-Julian oscillation which is both divergence and vorticity driven. Other examples are convectively coupled Kelvin waves and mixed Rossby gravity waves that are known to be strongly coupled to convection and interact with smaller scale moist gravity waves and meso-scale convective systems. The work could also be put in the more general context of MJO predictability studies, and seasonal to sub-seasonal predictions of tropical weather and climate variability. There is an abundant literature on these topics from the practical point of view and very little theoretical work. The questions of the existence-or-not of predictability limits and predictability sources for the MJO and tropical dynamics in general are still outstanding, and I have a feeling that this kind of work could help in the debate. This, in particular, could guide the choice and provide the necessary justifications for the parameter values used in the analysis. The paper could benefit from some discussion in the conclusion section and in the model setup on how the model and the presented results could be used or expanded to address these practical questions.
Specific comments:
1. Line 30: The assumption of constant divergence source amounts to neglecting the large-scale organization of convection and assuming that Rossby wave dynamics are separate from diabatically driven large-scale waves such as convectively coupled Kelvin waves and the MJO. This comment is not intended as a critic of the present work but instead to put a side note to say that in fact, convection organization itself has a predictability limit, and even the forced Rossby waves were predictable, it won’t guarantee the predictability of tropical dynamics as a whole.
2. Eqn 12 and Line 80: Instead of imposing a doubly periodic divergence term, the authors could try something that has a Gaussian shape in the meridional direction (that can be either symmetric or asymmetric as in Gill 1980) to remain in the spirit of tropical dynamics.
3. Section 3.1: Please say what n is here to remind the reader.
4. Line 110: The question remains as to whether this multiplicative nature will become a stabilizer rather than a chaos amplifier when divergence modes are allowed to vary and interact with the Rossby waves, as it is presumably the case for tropical dynamics.
5. Line 114: Why are they unrealistic? A sudden drop in phase speed is expected beyond the forcing wavenumber, which may lead to a large group speed!?
6. Line 115: By "there is no solution anymore", you mean that the numerical code blows up? Clearly, the dissipation parameter r has a say in this. How does its value impact the results?
7. Figure 2: Why is there a sudden drop in all the instability measures at the 0.08 mark and the oscillatory behaviour and sudden pickup just before 0.1?
8. Figure 4: Increasing n seems to have an overall stabilizing effect, although there are some outliers such as the case n=2.5 with the anti-symmetric forcing, which is by itself intriguing as it is unstable at small forcing and stable when the forcing is large. I wonder if the authors have an explanation or whether the analysis is actually insufficient for a full understanding of the model's behaviour.
9. Line 150: How do the higher resolution results compare to the low resolution ones presented in the previous sections? Why not do the analysis with this higher order projection?
Citation: https://doi.org/10.5194/egusphere-2026-3631-RC2
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