General comment

This paper investigates the connection between the occurrence of hemisphere-scale land surface temperature anomalies and the hemisphere-scale eddy meridional heat transport. One important and somewhat counter-intuitive result seems to be that often a small or even negative eddy heat transport is associated with co-occurring land surface heatwaves on the hemisphere. It would be interesting to put forth a hypothesis regarding the mechanism why this could or should be the case, and then use statistical analysis to support such a hypothesis. But that is not the topic of this paper.

Instead, the reader is offered a complex and detailed analysis of statistical connections between the meridional heat transport and the geographical patterns of several meteorological variables that appear when conditioning on extremes of this heat transport. The text and the plots in the result sections are meant to convince the reader that this analysis was done properly and they describe the geographical fields resulting from the analysis. I do not doubt that this was done OK. At the same time, it remained unclear to me what I am supposed to learn. In other words: what is the science question that you address?

To be sure, the authors make strong claims as to what their results mean, but I was not convinced by their arguments. In particular, I found bold causal inferences in the interpretation of the results, which in my eyes cannot be made based on a purely statistical analysis. When stripping away these causal claims, the reader is left with a number of statistical associations, but (as I said before) I was left wondering why these are interesting or important and in what sense they contribute to an understanding. That’s too bad, because the title says that enhanced “understanding” is the main point of the paper. My perceived lack of new insight weighs even more strongly given my feeling that the key question (see my first paragraph) remains unaddressed and unanswered. It may well be that this manuscript contains important insight, but it was impossible for me to recognize it from the current presentation. My central question is: what does this manuscript contribute to our understanding of hemisphere-scale land surface heat anomalies?

Possibly there is a hint at the underlying science question on line 48, namely that the authors “seek to understand how concurrent heatwaves…. are linked to extremes in planetary-scale Rossby wave anomalies….”, but in my eyes this goal is not achieved. The authors at best describe that concurrent heatwaves are linked to extremes in the meridional heat transport, but in my judgment this does not result in a deeper “understanding how” this works. In other words, the authors fall short of the goal set by themselves.

In addition, I have an issue with the part of the interpretation that concerns the occurrence of “troughs” and “ridges” on anomaly plots: a negative anomaly in pressure or geopotential does not necessarily imply a trough, it may just as well be a weaker-than-normal ridge. A similar issue is related to the occurrence and strength of jets.

Given my evaluation, I am skeptical that anything resembling this manuscript would be a useful scientific contribution to the field. I have a large number of detailed comments below which may help to clarify my criticism and which raise numerous further issues. Overall, I cannot recommend that this paper should be published in WCD.

Specific comments:

Line 29: How can an “episode” be related to a “frequency”?

Line 38: I find this formulation misleading: in what sense is resonance “facilitated” by the underlying conditions? It seems to me that your “underlying conditions” are simply the forcing for the waves, which (under specific conditions) undergo resonant amplification.

Line 44/45: what is the difference between “dynamical drivers” and a “process-based investigation”. To my taste this section contains too much jargon, and moreover I would welcome a more precise distinction between this work and previous work. Do you mean that your work merely analyses statistical connections rather than investigating the underlying dynamics? The latter could involve, e.g., linking observed phenomena with the underlying equations.

Line 63: what is a “rectilinear grid”, given that your domain is spherical?

Line 88, “correction for the wavenumber 0”: can you explain in a little more detail? What is the “zonal circulation”? You talk about a “vertical and meridional mean transport”, but isn’t the key here that you are considering a zonal mean transport?

Line 91: not clear to me what the word “this” refers to.

Line 99: Does table 1 refer to MHTs including all zonal wavenumbers?

Line 104: At first it did not become clear to me how you perform the “spatial average” of daily anomalies. Do you take the absolute value of an anomaly before you perform the spatial average? If not, warm and cold anomalies might cancel to a large extent. I presume that you do NOT take the absolute value, and that’s probably a main point of your analysis, but this should be made very clear to the reader.

Line 111: “Impact of MHT extremes on LST extremes”: this phrase is misleading, since it suggests that you can make a statement about causality…. which you cannot, based on a purely statistical analysis alone (see J. Pearl: The book of why). Correlation does not imply causation! Similarly on line 157 where you promise a “process-based understanding of mechanisms”, which would imply that you can distinguish cause and effect.

Line 111: What is a 2D-field at a grid point?

Line 114: “composite mean of such quantities”: not clear to me.

Table 2 and thereafter: is “LST | MHT” simply the number of cooccurring LST and MHT events?

Table 2: the last row contains bold-face entries with less than 10%, which seems to contradict the table caption.

Line140: given that according to Table 2 about 91.5% of all negative MHT extreme events in JJA are NOT associated with positive extreme LST events, it is not clear to me why the selection of events in the composites of Fig 1 is meaningful.

Line 146: It seems far-fetched to associate one single local pressure anomaly with the PNA pattern.

Line 147: “with respect to JJA”?

Line 148, “Accordingly”: how should the features on the LST plot associate with the features on the SLP plot? For me (not having read your previous papers) this is not obvious. Later in line 150 you state that this is somewhat “counterintuitive”.

Line 149 (and similarly in the abstract line 7), “….two deep troughs”: a negative SLP anomaly is not necessarily a trough, it may just as well be a weaker-than-normal ridge.

Line 151, “suppression of meridional exchange”: this seems to conflict with the fact that these plots are conditioned on events with extreme (negative) MHT: can you explain to the reader who has little experience with your previous work?!

Figure 1: I would appreciate axis labels with the respective longitude and latitude.

Line 156: it is not clear to me how this plot indicates the location and/or the strength of the jets.

Line 165: what is a “statistical simulation”?

Line 165, “the above mechanisms”: you just provided descriptions, I would not consider this as elucidating “mechanisms”.

Line 169: the paper that you refer to does NOT associated the actual episode of the Pacific heatwaves with resonance (rather, the authors associate a precursor event with resonance).

Line 178: It is not clear to me how you infer “blocking” from just looking at SLP anomaly patterns. What is your definition of “blocking”?

Line 187: how do you see a “branch of the jet stream” in a plot of wind-anomalies?

Fig 3a: Hovmoeller Plots? I can only see one plot. Also, it would be desirable to use a color scheme that clearly distinguishes positive from negative values.

Line 191: what would be a typical climatological value?

Fig 3b: what is the dashed line in that panel?

Line 192: at this point it is not clear (to me) how negative MHT can contribute to a local heat wave.

Line 196: “triggering” suggests a cause-and-effect relation, which however cannot be established from such a plot

Discussion of Fig 3: fine, but what am I supposed to learn from it?

Line 200, “was enhanced by a strong blocking…”: this was NOT shown

Line 219: it seems impossible to infer a “prerequisite” from just a single case.

Line 221, “fueled by”: what does this mean? A causal connection? Is the blocking caused by jet bifurcation, or is the jet bifurcation caused by the blocking, or are both caused by something else?

Line 222, 223: similar concerns (“enhance”, “trigger”)

Line 257: do you really select a “case study” (or maybe rather a case)?

Fig 8 called before Fig 7?

Lines 282/283: how can a reduced MHT be associated with energy convergence into the Arctic?

Line 297, “Jetstream bifurcation” is misleading, since the figure shows anomalies. In other words, the “bifurcation” may be part of the climatology and only be slightly stronger or weaker during the considered episodes.

Line 303 (and also abstract line 7), “location of troughs and ridges”: again (like above), a map that shows anomalies cannot make a statement about the location of troughs and ridges. In other words: a weaker-than-normal ridge is not necessarily a trough.

Line 315, “leads to”: do you imply a causal connection?

Line 321, “results in”: ditto.

Line 344: here it is not clear what is conditioned on what.

Line 348, “sufficiently strong to cause….”: how does this causal chain work? Do you ever in this paper give an explanation, or provide at least a hypothesis?

This study explores the link between concurrent hemispheric heatwaves (high Land Surface Temperatures, LST) and extremely weak Meridional Heat Transport (MHT) events. Authors present analysis for these combinations during boreal summer and winter, describing in detail the associated dynamical patterns across multiple variables, which they relate to existing literature. This descriptive approach is thorough, but the interpretation could be strengthened by drawing clearer connections to the study’s main research questions and hypotheses, which are not clearly formulated to begin with.

While the study tackles an important and timely topic, its current presentation limits the clarity and potential impact of its findings. The manuscript would benefit greatly from a clearer framing of the study’s goals and novelty early on, as well as a more integrated structure that better guides the reader through the analysis. In particular, introducing the central mechanism earlier and using schematic summaries would help contextualise detailed descriptions and improve overall readability. I therefore recommend a substantial restructuring to enhance narrative flow and ensure the scientific significance of the work is fully conveyed. See general comments for suggestions intended to be constructive.

General Comments

1. The introduction currently reads as though there is some confusion or inconsistency in how the authors position their work relative to existing literature and understanding. Authors write that they intend to explore link of LSTs to extremes in planetary-scale Rossby wave anomalies, which is a classic subject in atmospheric dynamics, yet at the l. 44 write “the literature [...] primarily focused on dynamical drivers,” implying that in this study they will not do so, but isn’t this study also examining dynamics? Perhaps the intention is to highlight that prior work has largely focused on Rossby waves as responses to atmospheric variability, without explicitly linking them to MHT processes. If so, I suggest clarifying this distinction. I recommend placing greater emphasis on the novelty of incorporating one large-scale thermodynamical mechanism (i.e. MHT). To strengthen this point, it would be helpful to include a statement highlighting that, to their knowledge, no prior study has specifically explored this linkage. That said, the study also engages with wave dynamics (e.g. wavenumber analysis), so care should be taken not to present the work as focused solely on thermodynamics. Emphasising the integration of thermodynamical and dynamical perspectives would more accurately reflect the study’s contribution. Also, is there a well-established hypothesis connecting moisture heat transport to (concurrent) heat extremes in Rossby wave anomalies? Or are the authors proposing or testing a new mechanism? This lack of clarity makes it hard to follow how the study’s “process-based investigation” (l.45) advances our understanding of co-occurring hemispheric heatwaves. Formulating specific research questions would go a great way to improve the clarity and goal of the paper.
2. Regarding Section 4
   • The explanation of the proposed mechanism is introduced only in the results section, and primarily through a case study. While I understand the use of a case study as a narrative device, in this context it would be more effective to introduce the mechanism earlier – ideally in the introduction – to better frame the study and guide the reader through the analysis. This could mean swapping the position of Sections 4 and 5, so that first we are presented with the overall picture, and then an example to show what a typical (or not typical) case might look like.
   • This section contains detailed descriptions that can be difficult to follow, but it remains unclear what they amount to. Adding a schematic (possibly even at the expense of Fig. 2) summarising the key processes, stages, and mechanisms – whether in the case study or the general explanation, whichever helps improve readability – would greatly help readers grasp the overall picture more easily. One schematic for the summer case and another later for the winter case.
3. As it stands, Sections 4–6 are very description-heavy, referring to multiple subfigures, variables, and seasonal differences. Because the results and discussion are presented as separate sections, it becomes difficult to digest and interpret the findings. A more integrated structure – e.g. combining results & discussion – could improve readability and help contextualise the findings as they are introduced. The schematic illustration suggested above could also aid in guiding the reader through the narrative.
4. Another possible restructuring tactic would be to subsume the current Sections 3–6 into a single Results section, with subsections (e.g. 3.1–3.4) capturing the existing material.
5. Towards the end of the study, authors suggest that the findings could help improve the predictability of certain events, it is currently not clear how this connection is established or supported by the results. That said, this might become more self-evident once the structure and contextualisation of the manuscript have been revised.

Specific comments

l.5 “other conditional occurrences” is too abstract and uninformative – what are these other occurrences?

l.17 and 24 The use of 'evidence' as a verb is technically correct but sounds unusual in contemporary academic English and may read as non-idiomatic. A more standard phrasing such as 'shows' or ‘highlights’ or 'provides evidence for' would improve readability.

l.38 “underlying conditions” is vague here, as it appears to group together two quite different types of factors: fixed geographic characteristics (orography and land-sea contrast) and low-frequency or slowly varying boundary conditions (sea surface temperature anomalies). The phrase could be amended to be more precise.

ll.51-6 See general comment recommendations for re-structuring.

l.80 Numbering missing for equations pertaining to wavenumber decomposition.

l.93 add space before ‘with’

l.96 add space after index"

Sect. 2.2.2. Some key details are missing or unclear in this paragraph for full reproducibility. Detrending and deseasonalisation are mentioned, but the specific methods used aren’t explained. It’s also unclear how the declustering is done – what parameters or window are used? Finally, more detail is needed on how the EVT-based convergence algorithm works in practice.

l.111 This sentence implies a directional, possibly causal relationship. I suggest using “association” instead of impact if the paper only shows statistical associations, and no causal analysis. If authors had introduced a clear hypothesised mechanism, then using terms like "impact" might feel more justified – even if causality isn’t fully proven.

l.114 “composite mean of such quantities in coincidence of LST|MHT” is a bit wordy – could simply write “composite mean of LST|MHT”

ll.111-114 “...whether the composite mean ... is random or reflects an emerging pattern.” Is somewhat vague. What is the null hypothesis? i.e. are co-occurring MHT extremes associated with significantly different conditions during LST extremes?

l.155 what counts as a “consistent deviation”?

l.118 Would suggest adding a reference to Wilks (2016).

ll.119-20 Significantly different the OVERALL distribution? So are you testing LST|MHT against LST|‾MHT‾ or climatology? Please clarify.

l.122 “weak MHT extreme” sounds contradictory. If the intended meaning is “extremely weak MHT values (i.e. very low MHT, and not non-extreme or moderate), then a clearer phrasing would be “extremely weak MHT” or possibly “strongly negative MHT anomalies” or “lower-tail MHT extremes.” I suggest considering one of these alternatives throughout the manuscript.

Table 2. Last row highlights values below 10%, in contradiction with caption.

ll.126-9 What is the implication for your study of the statement in the sentence starting “However, [...]” with regard to the strength of the association between MHT -> LST ?

l.128 “consecutive days” is more standard phrasing in this context.

ll.130,133  “weak MHT-warm LST” is the same as LST₉₅|MHT_↓, correct? I suggest sticking with the latter ‘symbolic’ notation throughout the text for clarity and consistency. Reverting to mixed phrases like the former can easily lead to confusion, especially when other conditions (like strong MHT) are also discussed.

ll.130-33 One of the study’s key claims regards LST₉₅|MHT_↓ accounts for 30% and 40% of warm LST days in JJA and DJF, respectively. However, this paragraph suggests that these figures come from a fraction of heatwaves, whose total durations make up that proportion of LST days. If so, I think this deserves clearer framing – the current phrasing risks implying that individual LST₉₅|MHT_↓ days make up that share, rather than those days occurring within longer events. I recommend clarifying whether the percentages refer to discrete days or to the cumulative duration of events in which LST₉₅|MHT_↓ conditions are observed. This is a presentation issue, not necessarily a flaw in the result, but it risks misleading interpretation.

Figure 1. I suggest reordering the figure panels so that the same variable is shown side by side across seasons. This would make seasonal differences easier to compare at a glance.

l.156 The interpretation of wind speed anomalies is not straightforward when trying to infer changes in the jet stream's absolute strength or position. A positive anomaly simply indicates stronger-than-average winds at a given location, but this can mean very different things depending on the climatological mean – e.g. in climatologically weak-jet regions, it may reflect modest flow or jet extension, while in strong-jet regions, it could signal true intensification or a shift in jet position. I suggest supplementing the V250 fields with contours of absolute wind fields or some baseline seasonal climatology.

ll.177-8 The authors attribute the pattern to strong blocking based on SLP anomalies. However, since blocking is generally diagnosed using mid- to upper-tropospheric geopotential height or potential vorticity. I suggest either supporting this claim with such fields or rephrasing to avoid implying a definitive blocking event based on surface pressure alone.

ll.186-7 See my comment regarding l.156.

Figure 3. I recommend increasing the font size of all text and labels, as well as increasing the thickness of curves in Fig. 3b to improve visual communication. Additionally, Fig. 3a title says MHT anomalies, but the caption says absolute MHT. Please clarify.

l.219 Are authors making this claim based on the one case?

l.258 Double-check WCD’s stylistic guide for dates: I think “19 January 2007” without ‘th’ may be correct.

l.274 “O” letter instead of “0” number in ENSO

ll.299-300 What are the implications of these observed differences? Clarifying this sentence would strengthen the connection between the diagnostics and the study’s core questions –  which, as currently presented in the introduction, are not that clear and could benefit from sharper formulation.

ll.322-6 This is precisely the kind of information that could be part of a summarising schematic.

ll.328-31 An interesting hypothesis that would be worthwhile testing in future research!

l.345 The phrase “other combinations” is vague and uninformative. I recommend briefly restating the specific combinations for clarity, even if this involves some repetition.

l.348 Once again, I would hesitate to mention causality.

Figure 7b and various in panels Figure 9. Some anomalies exceed the colorbar range, resulting in blank or clipped areas in the plots.