the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Jun 2026
Three-dimensional atmospheric circulation teleconnections in the Northern Hemisphere
Abstract. Atmospheric circulation teleconnections play a critical role in modulating low-frequency climate variability and driving regional extreme weather events, such as summer heatwaves. However, traditional teleconnection indices are predominantly defined using two-dimensional horizontal variables, which inadequately represent the dynamically crucial coupled vertical circulations. Here, we establish a three-dimensional analytical framework by applying the teleconnection method to the meridional and zonal vertical stream functions (H and W) derived from the three-pattern decomposition of global atmospheric circulation (3P-DGAC). We identify 14 structurally distinct vertical teleconnection patterns in the Northern Hemisphere mid-high latitudes, which demonstrate robust validity in reconstructing summer surface air temperature (SAT) and hemispheric circulation fields (yielding mean spatial correlations of 0.64 and 0.60, respectively, over 1979–2022). The proposed three-dimensional teleconnections effectively capture the low-frequency atmospheric variability that modulates Northern Hemisphere summer climate. Ultimately, this framework provides a unified dynamical perspective for understanding seasonal climate variability and offers a robust approach for diagnosing the atmospheric circulation mechanisms underlying regional temperature extremes.
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Status: open (until 13 Sep 2026)
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RC1: 'Comment on egusphere-2026-2824', Anonymous Referee #1, 08 Aug 2026
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AC1: 'Reply on RC1', Shujuan Hu, 09 Sep 2026
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We sincerely thank the reviewer for the constructive comments. These suggestions have been very helpful in improving the clarity and rigor of our manuscript. We have carefully addressed each comment and revised the manuscript accordingly. Our point-by-point responses are provided in the attached file.
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AC1: 'Reply on RC1', Shujuan Hu, 09 Sep 2026
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RC2: 'Comment on egusphere-2026-2824', Anonymous Referee #2, 21 Aug 2026
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Summary
The authors introduce a novel three-dimensional analytical framework to identify vertical teleconnection patterns in the Northern Hemispheric summer. By applying the teleconnection method to the meridional and zonal vertical stream functions derived from the three-pattern decomposition of global atmospheric circulation (3P‑DGAC), the authors identify 14 distinct teleconnection patterns. They demonstrate that these patterns can effectively reconstruct summer surface air temperature and large-scale circulation anomalies, offering a new perspective on low-frequency variability. The framework is innovative and the results are scientifically intriguing, particularly the reconstruction skill for extreme heat years. However, the manuscript currently lacks a solid physical explanation for the proposed patterns, specifically regarding their dynamical origins and their relationship to established teleconnections. To ensure the robustness and physical relevance of these new indices, a revision is necessary.
Specific Comments
1, The manuscript identifies 14 new teleconnection patterns based on statistical correlation, but it provides limited physical justification for their existence and maintenance. To demonstrate that these patterns are physically consistent with large-scale dynamics rather than merely statistical constructs, I recommend adding a Rossby wave activity flux analysis. This analysis would help visualize the propagation of wave energy associated with these vertical patterns, confirming whether they behave as true dynamical modes.
2, The identification of vertical circulation cells is a key contribution of this work, but the physical drivers remain unclear. The manuscript should at least discuss the possible physical processes maintaining these vertical cells. Are they driven by diabatic heating, orographic forcing or land-atmosphere interactions? A brief dynamical interpretation would significantly strengthen the proposed framework.
3, The authors argue that several patterns correspond to known modes like the Silk Road Pattern (SRP), British–Baikal Corridor (BBC), and circumglobal teleconnection (CGT). I suggest to provide a summary table or schematic that explicitly maps the new 3D patterns to previously known teleconnections (SRP, CGT, BBC, BOC, Summer NAO) with key references. This will help readers quickly understand the hierarchy and novelty of your findings.
4, Does the 3D perspective reveal previously underappreciated vertical structures for these known patterns? Or are these entirely new modes? If the latter, the manuscript should argue why these significant modes were missed by traditional 2D frameworks.
5, Could you provide the explained variance for each of the 14 teleconnection patterns? It is crucial to know which patterns are the most dominant and statistically significant to assess their relative importance in the climate system.
Citation: https://doi.org/10.5194/egusphere-2026-2824-RC2 -
AC2: 'Reply on RC2', Shujuan Hu, 09 Sep 2026
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We are very grateful to the reviewer for the thoughtful and constructive feedback. The suggestions have been extremely useful in strengthening the scientific rigor and overall quality of the manuscript. We have carefully considered all comments and incorporated the corresponding revisions. Please find our detailed, point-by-point responses in the attachment.
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AC2: 'Reply on RC2', Shujuan Hu, 09 Sep 2026
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This study develops a three-dimensional perspective for characterizing Northern Hemisphere summer teleconnections by applying the conventional teleconnectivity method to the meridional and zonal vertical-circulation streamfunctions derived from the 3P-DGAC framework. Fourteen vertical-circulation teleconnection patterns are identified, and their associated horizontal circulation and surface air temperature signatures are examined. The study provides a potentially useful unified framework for connecting vertical circulation cells with several familiar horizontal teleconnection patterns, including the Silk Road Pattern, the British-Baikal Corridor, the British-Okhotsk Corridor, and the summer NAO. The reconstruction analyses further illustrate the diagnostic value of these patterns for Northern Hemisphere circulation and surface temperature variability.
Overall, I find the perspective interesting and potentially valuable. The principal contribution, in my view, is the provision of a unified three-dimensional framework through which both established and less familiar teleconnection structures can be examined. The manuscript is generally suitable for publication after minor revision. I have the following comments.
1. Robustness of the teleconnections identified near the pole
Several identified patterns, including HP and WCV, have one or both endpoints at very high latitudes. In some cases, the two endpoints also appear to be separated by a relatively short physical distance. Because meridians converge toward the pole, grid points that are well separated in longitude may nevertheless be geographically close. Moreover, the regular latitude-longitude grid strongly oversamples the polar cap in terms of grid-point density. These features raise the possibility that some of the identified pairs represent a local dipolar structure, spatial autocorrelation, or a gridding-related artefact rather than a genuine remote teleconnection. A brief sensitivity test using a reasonable minimum separation, an equal-area or latitude-weighted treatment, or exclusion of the immediate polar cap would help establish the robustness of these high-latitude patterns.
2. Nomenclature and relationship to established teleconnection patterns
The use of 14 geographically based abbreviations, such as WMCS, WWSJ, WGA, and WCV, makes the manuscript difficult to follow, especially when several indices appear together in the reconstruction analysis. The additional use of “HP” both for the Polar I pattern and as an abbreviation for “horizontal pattern” further increases the potential for confusion.
I recommend adding a summary table containing, for each pattern: its full name and abbreviation, whether it is based on (H) or (W), the coordinates of its two endpoints, and its closest previously established teleconnection counterpart. Where such a counterpart exists, the corresponding spatial correlation could also be included. This would allow readers to understand more clearly which patterns provide genuinely new information and which represent a three-dimensional reinterpretation of familiar modes.
3. Dependence and possible redundancy among the 14 indices
The 14 patterns are identified separately from the (H) and (W) streamfunctions and are not constrained to be mathematically orthogonal. It is therefore important to establish whether some indices describe closely related aspects of the same underlying circulation variability. This issue is also relevant to the subsequent stepwise regression and reconstruction analyses.
The authors should provide, at minimum, a correlation matrix among the 14 indices and discuss any substantial dependence or clustering among them. It would also be useful to clarify whether the (H)- and (W)-based patterns can be regarded as distinct modes or, in some cases, as different projections of the same three-dimensional circulation system. The manuscript should avoid implying that all 14 patterns are dynamically independent unless this can be demonstrated.
4. Out-of-sample robustness of the reconstruction
The teleconnection patterns, regression coefficients, predictor selection, and reconstruction skill appear to be derived and evaluated over essentially the same 1979-2022 period. The reported spatial correlations may therefore partly reflect in-sample fitting, particularly given the relatively short record and the use of stepwise regression with 14 potential predictors.
A leave-one-year-out or comparable cross-validation would provide a more convincing estimate of reconstruction skill for both SAT and circulation anomalies. At least the 2022 reconstruction should be performed without using 2022 in the estimation of the regression coefficients. If redefining the complete teleconnection patterns within every training sample is impractical, the authors should clearly distinguish between pattern definition and regression fitting and acknowledge the remaining in-sample component of the analysis.
5. Potential application to seasonal prediction
The demonstrated relationship between these modes and Northern Hemisphere summer SAT raises an interesting question regarding their practical predictability. Can seasonal forecast systems predict the amplitudes of these three-dimensional teleconnection indices, and would an index-based reconstruction provide useful SAT prediction skill beyond the model climatology or conventional circulation indices?
A full forecast experiment may be beyond the scope of the present revision. Nevertheless, the authors could provide a preliminary assessment using an available seasonal hindcast dataset, if feasible, or otherwise expand the discussion to formulate this as a concrete future application. In the absence of a hindcast evaluation, statements that improved representation of these modes would enhance forecasting skill should be appropriately qualified as a hypothesis rather than a demonstrated result.
6. Consistency and presentation
Several internal inconsistencies should be corrected during revision. For example, 1979-2022 contains 44 summers, whereas the manuscript refers to a “43-year mean spatial correlation.” Figure 5 gives 1979-2018 in its caption, although the main analysis period is stated as 1979-2022. The ordering of the (W)-based patterns in some figure captions also appears inconsistent with the panel labels and the discussion in the text. The reference to HP-HUB in Fig. 2b should be checked, as this pattern appears to be shown in another panel. Finally, the description of the manuscript structure at the end of the Introduction does not match the actual section numbering. A careful proofreading of the pattern names, panel references, duplicated words, and analysis periods is needed.