the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Apr 2026
Subtropical Extreme Heatwave Dynamics in the Intermediate-Complexity Atmospheric Model Aeolus 2.0
Abstract. Heatwaves in the subtropical and mid-latitude regions, which arise from localized heating can ripple through the atmosphere and persist for weeks, yet the mechanisms behind this chain of events remain difficult to disentangle. Here we use the Aeolus 2.0 model, which is a moist-convective thermal rotating shallow-water (mcTRSW) framework of intermediate complexity, to explore how buoyancy anomalies evolve under both dry and moist conditions, innovatively including background effects to enhance realism. We find that localized heating sets off a rapid atmospheric adjustment: air converges near the surface, diverges aloft, and quickly organizes into paired cyclonic (lower layer) and anticyclonic circulations (upper layer). Earth’s rotation then distorts these structures, producing asymmetries, spiral rainbands, and rainband-driven feedbacks. Moist convection greatly amplifies this response by releasing latent heat, which fuels sustained instability and rainfall organization. Inertia–gravity waves emerge as a key pathway for redistributing heat and momentum, while Rossby waves and beta gyres gradually reshape anomalies, tilting them poleward and breaking them into smaller vortices. The simulations also reproduce well-known observational signatures, including comma-shaped water vapor patterns and mesoscale vortices. Together, these results show how a simple localized heat source can trigger a cascade of atmospheric responses that link convection, wave dynamics, and large-scale circulation. By capturing these processes, Aeolus 2.0 provides a bridge between theoretical frameworks and full climate models, offering new insight into the dynamics that sustain extreme heatwaves in a warming world.
- Preprint
(7928 KB) - Metadata XML
-
Supplement
(18398 KB) - BibTeX
- EndNote
Status: open (extended)
-
CC1: 'Comment on egusphere-2026-512', Saeed Hariri, 21 May 2026
reply
-
AC1: 'Reply on CC1', Sullyandro Oliveira Guimarães, 25 Jun 2026
reply
Dear Reviewer,
Thank you for taking the time to review our manuscript and for your detailed feedback and recommendations. We have carefully evaluated all your comments, and our point-by-point responses and explanations are compiled in the attachment.
-
CC2: 'Reply on AC1', Saeed Hariri, 11 Jul 2026
reply
Reviewer assessment of author responses
Manuscript egusphere-2026-512
“Subtropical Extreme Heatwave Dynamics in the Intermediate-Complexity Atmospheric Model Aeolus 2.0” (Guimarães, Rostami, Petri)
Recommendation after author response: Minor revisions
Overall assessment
I thank the authors for their constructive and detailed responses. Taken together with the Supplement and the Zenodo repository, the replies address the substance of my main concerns: the topography development is shown to be present in the code, the numerical configuration has been specified, and the authors confirm that quantitative wave diagnostics (energy propagation, group velocity, wave–wave interactions) already exist for every case. I am satisfied that the underlying model and experiments are sound and that no new simulations are required.
However, most of this information currently lives in the responses, the Supplement, or the repository rather than in the manuscript, and a few claims and inconsistencies still need to be tightened. The gap between “the authors can answer these questions” and “the paper answers these questions” is real for a model-description paper, and closing it is more than a cosmetic pass. I therefore recommend moderate (minor) revisions: the changes are well defined and achievable in one round, but they are substantive enough that I would like to see the revised manuscript before it proceeds.
Point-by-point evaluation of the major comments MC1 — Model-development focus / distinguishing inherited vs. new equations
Substance addressed; the paper must now carry it.
The topography explanation and the concrete code reference (aeolus2main.py, variable Dh10, the ⟨∇pᵢ⟩ formulation on lines 125–129) resolve where the new development lives, and the contrast with Rostami et al. (2023) is a clear statement of novelty. In the revision I ask the authors to add a short paragraph or compact table separating (1) inherited mcTRSW equations, (2) established Aeolus 2.0 developments, and (3) additions specific to this paper, and to state briefly how ERA5 fields are projected onto the two-layer (hᵢ, bᵢ, vᵢ) variables.
Because a central result is the inertia–gravity-wave burst, please also state explicitly whether the imposed α-Gaussian anomaly is introduced in balance or as an intentionally unbalanced perturbation, so the burst is correctly understood as the adjustment of that anomaly. I note and credit that all fields are shown relative to a reference run, which cancels the background spin-up shock; please make that point explicit in the text, as it underpins the interpretation of the difference fields.
MC2 — Numerical configuration
Answered in the response; must be moved into the manuscript, with inconsistencies reconciled.
The reply provides grid (384 × 768, ~0.5°), 1-minute timestep, 4 outputs/day, ~102-day runs, per-case cost (~3 h, 20 GB), Dedalus v2.2207.3 under Python 3.10.14, and library versions. This answers reproducibility and should become a dedicated numerical-implementation subsection. Please add the dissipation/dealiasing scheme and the stability basis for the 1-minute step, which remain unstated.
Two internal inconsistencies to fix: “102 numerical-days (4× per day = 408 time-steps)” conflates output frames (408) with integration steps (~1.5 × 10⁵ at Δt = 1 min); and the run is described as “16 cores / 16 GB RAM” while the machine is given as a 24-core / 32 GB system. Please report one consistent configuration.
MC1/MC2 — Numerical geometry: reconcile before publication
Clarification required.
Figure 1 states the solver uses the spin-weighted spherical harmonics method, whereas the MC2 response describes a Cartesian domain processed with Fourier series, and Eq. (3)/line ~158 imposes a no-normal-flux boundary condition (implying a bounded domain, not a periodic sphere). Please state unambiguously the coordinate system and spectral basis, the latitude-grid type, and the meridional/pole treatment. This bears directly on the β-gyre, Rossby-wave, and equatorward IG-propagation claims, so it should be settled explicitly rather than left to the figure schematic.
MC3 — Validation
Expected addition, not optional.
The authors confirm that quantitative wave diagnostics exist for all cases in the repository. For a model paper, at least the key ones should appear in the manuscript. Concretely, I ask the revision to include: (i) energy conservation for the dry adiabatic runs (a direct verification the authors already have); (ii) a numerical value for the external/barotropic L_d at 20°N to support the “~32° aligns with the deformation radius” statement, which is currently asserted; and (iii) one or two of the already-computed wave-propagation diagnostics (e.g., group velocity or phase speed) compared against shallow-water expectations. None of this requires new runs, but it is what moves the validation from qualitative to quantitative, and it is the main reason I am recommending moderate rather than minor revisions.
MC4 — “Heatwave” terminology and framing
Wording change expected.
Please soften the title and abstract framing toward idealized buoyancy-anomaly dynamics relevant to subtropical blocking and heatwave-like circulation responses, given that land–atmosphere coupling, radiation, and boundary-layer processes lie outside the model’s scope. This does not affect the results.
MC5 — Qualitative interpretation
Addressed; light tightening expected.
The pointer to divergence and wind diagnostics is noted. Please scale terms implying resolved fine-scale structure (“mesoscale convective systems,” “frontal boundaries,” “rainfall organization”) to what a two-layer ~0.5° model actually represents, or tie them explicitly to the supporting diagnostics.
MC6 — Mathematical notation
Copy-edit; confirm one specific fix.
Please confirm the intended form of Eq. (4b), which as printed lists δℋ/δv_k twice with different right-hand sides.
MC7 — Figures
Copy-edit.
The caption, colorbar, and vector-scaling improvements described in the response are sufficient; I will confirm in the revision.
Two points to clarify on the novelty claims
These are clarifications, not new work. First, since the experiments are centered over the open North Atlantic (20°N, 40°W), please state whether the bottom-topography height h_b is nonzero anywhere in the shown runs; if it is effectively zero, the topography capability should be presented as a documented model feature rather than a demonstrated result of this paper. Second, the background-flow novelty is conveyed most directly by indicating where its effect is isolated; if a background-on/background-off contrast already exists among the runs, a brief mention would substantiate the claim.
Specific comments
The remaining specific comments (Abstract and Introduction framing, Section 2.1 tables of prognostic variables/parameters/scales, the symbol–parameter table, Section 2.2 / Eq. 5 typesetting and definition of the α-Gaussian, softening “validates the approach” in the Conclusions, and a language pass) are well defined and can be handled in this revision. The Section 2.1 tables and the symbol table in particular would substantially improve readability.
Summary
The science and the model are sound, and the author responses resolve the questions of substance; what remains is to bring that substance into the manuscript and to tighten a few claims. For the revision I ask the authors to:
- move the numerical-configuration and topography details into the paper, and reconcile the inconsistencies (geometry statement; steps vs. output frames; cores/RAM);
- add the quantitative validation elements above — dry-case energy conservation, a numerical L_d value, and one or two of the already-computed wave diagnostics;
- clarify whether topography and background flow are active/isolated in the shown experiments;
- state whether the imposed anomaly is balanced, and make the reference-run differencing explicit;
- soften the “heatwave”/“validates the approach” framing;
- correct Eq. (4b), improve the figure captions, and complete a language pass.
These are achievable in a single round, and I look forward to reviewing the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-512-CC2
-
CC2: 'Reply on AC1', Saeed Hariri, 11 Jul 2026
reply
-
AC1: 'Reply on CC1', Sullyandro Oliveira Guimarães, 25 Jun 2026
reply
-
RC1: 'Comment on egusphere-2026-512', Anonymous Referee #1, 17 Jun 2026
reply
Dear editor,
Thank you for the opportunity to review the manuscript. I would like to recommend the article titled “Subtropical Extreme Heatwave Dynamics in the Intermediate-Complexity Atmospheric Model Aeolus 2.0” for publication after minor revision.
The authors employ the intermediate-complexity multilayer moist-convective Thermal Rotating Shallow Water (mcTRSW) ( Aeolus 2.0 framework) to investigate the dynamics of localized buoyancy anomaly driven extreme heatwaves in the subtropical atmosphere. The study systematically conducts idealized numerical simulations across a multi-dimensional parameter space, including dry/moist convection, barotropic/baroclinic configurations, and weak/strong anomaly amplitudes. The results present a range of dynamical phenomena, including the initial adjustment process, the propagation of inertia–gravity waves, the simultaneous generation of cyclonic and anticyclonic circulations, and the evolution of precipitation structures, while also reproduce several canonical observational signatures, including comma-shaped water vapor patterns, spiral rainbands, and mesoscale vortices. Overall, the topic is of scientific interest, and the manuscript is generally well organized. But I have several comments about the paper.
Comments:
1. The authors do not report the functional form (f-plane or β-plane) or the numerical values of the Coriolis parameter used in the model and numerical simulations.
2. The authors explicitly state in the ConclusionsSection that "Compared to studies based on earlier versions of our model, adding certain real-world characteristics, such as topography and background wind velocity effects, in a novel development that improves the fidelity of the experiments”. However, upon careful examination of the full manuscript, no mathematical formulation, numerical implementation, or diagnostic analysis of topographic effects is provided anywhere in the text. If topography was indeed implemented, the authors should provide its mathematical formulation, implementation details, and a sensitivity analysis demonstrating its impact. If not, the reference to topography should be removed from the novelty statements and, if appropriate, moved to the future work section.
I have found some minor issues in the manuscript.
1. Page 10 line 225: Additional zonal and meridional divergence temporal evolution--->Additional zonal and meridional divergence temporal evolutions
2. Page 11 line 274: extremes scenarios--->extreme scenarios
3. Page 12 line 279: the strong cases shows--->the strong cases show.
I recommend acceptance of the manuscript after minor revision.
Citation: https://doi.org/10.5194/egusphere-2026-512-RC1 -
AC2: 'Reply on RC1', Sullyandro Oliveira Guimarães, 25 Jun 2026
reply
Dear Reviewer,
Thank you for taking the time to review our manuscript and for your detailed feedback and recommendations. We have carefully evaluated all your comments, and our point-by-point responses and explanations are compiled in the attachment.
-
AC2: 'Reply on RC1', Sullyandro Oliveira Guimarães, 25 Jun 2026
reply
Model code and software
Materials for the article Sullyandro O. Guimarães, Masoud Rostami, Stefan Petri https://doi.org/10.5281/zenodo.18065000
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 319 | 92 | 30 | 441 | 70 | 19 | 21 |
- HTML: 319
- PDF: 92
- XML: 30
- Total: 441
- Supplement: 70
- BibTeX: 19
- EndNote: 21
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Dear Authors,
Please find attached my review report. The report contains my detailed comments and recommendations regarding the manuscript.