General Comments

This is a well-structured preprint that presents a detailed and thoughtful analysis of the role of synoptic circulations in shaping dry static energy (DSE) variability over a South Asian heatwave hotspot. I particularly appreciated Figures 8 and 9, which offer a clear and compelling visualisation of the circulation regimes linked to different phases of DSE evolution. These figures, together with the accompanying explanations, effectively translate complex dynamical interactions into an intuitive framework. The numbered summary of key findings is also well-executed and helps ground the reader in the main contributions of the study.

One area for improvement lies in the connection between the paper’s motivation and its core analysis. The introduction sets up an expectation that the study will explore links between circulation and the distribution of near-surface temperature, particularly the behavior in the tails. However, the main focus is on the daily tendency of lower-tropospheric DSE (δS), without explicitly returning to the temperature distribution itself. While δS is a justified and meaningful proxy, this disconnect could be addressed either by more explicitly linking δS back to the statistical behavior of near-surface temperature. Even if this is just elaborating on the different stages in a lifecycle of a DSE anomaly hinted at in Fig 8f and 9g.

Specific Comments

• Is there a reason why Fig 8f does not have a row for NL Growth (listed on line 431)?
• On Line 253, says similar results for both March and April. Maybe to cut down on figures could present entire analysis for just April  i.e. no Figure 2, or combined March and April as done in Figure 1.
• I think it would be clearer to explitly define what you mean by a quasi-linear vs non-linear contribution to dS. Maybe in Fig S1, you could colour the contributions based on which category they belong to.
• I think there the amount of plots in figure 4 could be reduced. Possibly just showing Figure 4e, but with switch x and y axis, and then have vertical lines or shading to highlight decile 1 and 10.
• I think the supplementary information would be easier to read if all the information required for a particular figure or was given in the figure caption, rather than giving the information first and then showing the figures.
• To make clear the results of Figure 8, It could be interesting to show a schematic of the growth of a given heatwave event, and the expected growth or decay regimes at different stages of its lifetime based on Fig 8f. Or someway to make Fig 8f and 9g clearer. I find the shading in Fig 8f and Fig 9f a bit confusing, maybe make Fig 9f blue  and darker blue means more negative S'.

Technical Corrections

• Red is negative in Figures 3a and 4a but positive in Figures 2b,  3b, 5a,b,c,d. I think it would make sense to have blue negative, grey neutral and red positive everywhere.
• In Figures 2,3 and 5 I think it may be clearer to just number the leaf nodes.
• Fig S7 - No axis labels
• Fig S9 - Might be interesting to show decile 1 and 10 in different colour, stacked on top of each other.
• I would be easier to read if the figures were mentioned in the text in the order that they are shown. At the moment, the first figure mentioned is Fig 2 and the first supplementary figure mentioned is Fig S5.
• Typos
  • Line 253 - preenting
  • Line 180 - Supplimentary
  • Line 313 - secondory 

This draft studies how synoptic-scale circulation affects day-to-day lower-tropospheric dry static energy (DSE) variations through advection processes in a South Asian region, which in turn modulates heatwaves on surface. This draft uses the decision tree model to classify day-to-day DSE variations into different classes based on different DSE advection terms.  Quasi-linear DSE advection terms are found to determine the sign of day-to-day DSE variations, while nonlinear advection terms determine the magnitude of extreme day-to-day DSE variations in tails of the distributions. This draft also performs composite studies of the circulation patterns corresponding to different classes from the decision tree model. This draft provides detailed insights into the circulation patterns responsible for the South Asian heatwaves, and the methodology could be applied to other regions. However, several points need to be clarified before publication.

The version I review is https://essopenarchive.org/users/905720/articles/1280266-the-role-of-synoptic-circulations-in-lower-tropospheric-dse-variability-over-a-south-asian-heatwave-hotspot?commit=4cea58bef2f3c3172fe26803a8031b5fe5008c9b

Major comments:

1. This draft assumes that the day-to-day surface temperature variations are dominated by DSE advection processes. It is true that Figure 1 indicates a strong correlation between them, but the correlation does not show the dominance of DSE advection processes. Imagine a case where DSE advection processes always contribute to 20% of temperature variations, they would still have a positive correlation, but the temperature variations are dominated by other processes. The authors should quantify how much DSE advection processes contribute to temperature variations – for example, convert the x-axis in Figure 1(a) to a corresponding temperature variation and show all points are close to the 1:1 line.

1. A related question: Previous work (Quan et. al., 2023, https://journals.ametsoc.org/view/journals/clim/36/15/JCLI-D-22-0556.1.xml) showed that diabatic processes (e.g. latent heating related to phase change), rather than horizontal dry advection processes, are responsible for extreme lower-tropospheric DSE and heatwaves especially in coastal monsoon regions. I understand this draft mainly focuses on the role of dry advection, but more discussions and comparison with the previous work are needed to explain why dry advection plays a dominant role and diabatic processes could be ignored in the zeroth order.

1. I do not fully understand the motivation and advantages for using the decision tree model. By doing simple conditional mean composites based on the signs or deciles of different advection terms, one could also look at different circulation patterns across the distribution of DSE advection terms. Besides, as shown in figure 2 and 3, 25% of the incidents in node 2 and 6 are not “negative” or “positive” events, so the leaf nodes are not clean classes. I suspect composite analysis of such classes with mixed events does not yield accurate descriptions of physical processes governing positive or negative DSE variations.

1. With many DSE advection terms (i.e., dimensions of features), one can arbitrarily control the depth of the decision tree, and somehow argue that the leaf nodes represent different classes. Why does 5 leaf nodes behave better than 4 (a shallower tree) or 10 (a deeper tree) in figure 5? The authors might have some early-stop criteria to avoid over-fitting, which should be justified explicitly.  

1. A related question: In Figure 8 I think the circulation patterns and DSE advection processes are almost identical between (a and (c, as well as between (d and (e. The authors should justify that they are different classes physically rather than an over-fitting effect.

Minor comments:

1. Equation 1a and 1b: The authors should quantitatively justify that the non-divergent approximation is reasonable.
2. Equation 3d only has eddy-mean terms and the eddy-eddy term. Why is the mean-mean term ignored?
3. Why is the eddy-mean term in equation 3d named the “quasilinear” term, not the linear term?
4. Line 266 and 282: Composite circulation maps, perhaps in the SI, will make the two kinds of deviations easier to understand.
5. Line 358: The full-stop in the middle should be removed.
6. Line 378: These findings finding underscore …