Constructing Extreme Heatwave Storylines with Differentiable Climate Models

Whittaker, Tim; Di Luca, Alejandro

doi:https://doi.org/https://doi.org/10.48550/arXiv.2506.10660

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https://doi.org/https://doi.org/10.48550/arXiv.2506.10660

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12 Aug 2025

| 12 Aug 2025

Status: this preprint is open for discussion and under review for Weather and Climate Dynamics (WCD).

Constructing Extreme Heatwave Storylines with Differentiable Climate Models

Tim Whittaker and Alejandro Di Luca

Abstract. Understanding the plausible upper bounds of extreme weather events is essential for risk assessment in a warming climate. Existing methods, based on large ensembles of physics-based models, are often computationally expensive or lack the fidelity needed to simulate rare, high-impact extremes. Here, we present a novel framework that leverages a differentiable hybrid climate model, NeuralGCM, to optimize initial conditions and generate physically consistent worst-case heatwave trajectories. Applied to the 2021 Pacific Northwest heatwave, our method produces heatwave intensity up to 3.7 °C above the most extreme member of a 75-member ensemble. These trajectories feature intensified atmospheric blocking and amplified Rossby wave patterns—hallmarks of severe heat events. Our results demonstrate that differentiable climate models can efficiently explore the upper tails of event likelihoods, providing a powerful new approach for constructing targeted storylines of extreme weather under climate change.

Received: 01 Aug 2025 – Discussion started: 12 Aug 2025

Tim Whittaker and Alejandro Di Luca

Status: open (until 31 Oct 2025)

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RC1:
'Comment on egusphere-2025-3748', Anonymous Referee #1, 14 Sep 2025 reply
Dear Editor,
Thank you for inviting me to review this manuscript. Please find below my comments and suggestions to the authors.
General Comment
First of all, I would like to thank the authors for investigating the promising field of finding alternative, less-computationally demanding tools for simulating extreme events. The overarching aim of the study is timely and well chosen.
In this paper, the authors propose a method to simulate storylines of extreme weather events by perturbing the initial conditions of the hybrid climate model NeuralGCM, which is differentiable and therefore amenable to gradient-based optimization. Their framework identifies small but plausible initial perturbations that evolve into more extreme heatwave trajectories. As a proof of concept, the method is applied to the 2021 Pacific Northwest heatwave (PNW2021). The optimized runs produce heatwaves that are up to 3–4 °C hotter than any member of a 75-member stochastic NeuralGCM ensemble, with strengthened blocking and Rossby wave patterns consistent with known physical mechanisms. Importantly, the required perturbations remain within ensemble variability, suggesting plausibility.
The methodology is promising, and I consider the article worthy of publication after revisions. My general impression is that the material is interesting but the presentation sometimes makes it difficult for readers to follow, particularly in Sections 2 and 3, which should undergo some changes. By contrast, I found the Discussion (Section 4) concise, clear, and well situated within the literature. Below, I provide more detailed comments that I hope will help the authors clarify and strengthen the manuscript.
Specific Comments
Section 2.1
Please expand this subsection. It is helpful to introduce the methodology formally, but currently it lacks clarity and rigour. For non-mathematical readers, the description is particularly difficult to follow.

At the beginning, one or two sentences reminding the reader of the subsection’s aim (why optimization is needed and what problem it addresses) would help.

Some notations are undefined (e.g., x^i_0). Please define all variables consistently.

The authors state that Eq. (3) is a good loss function. Could you explain why this particular form is appropriate for this case study, and why alternatives were not chosen?

Please state explicitly what O(X(t)) and F(O(X(t))) represent for this case study.

The term “component” is ambiguous—please clarify what is meant.

Why was a 5-day averaging window chosen? Is this linked specifically to PN2021, or more generally to temperature autocorrelation?

In Eq. (3), what does the index i represent, and what does it span over? Similarly, please define \gamma and \theta (I assume latitude and longitude).

I find it misleading to call the first term the “heatwave intensity term” when “heatwave intensity” is formally defined later in Section 2.3 but not being the same object.

The “objective function” mentioned after Eq. (3) should be clearly defined.

Section 2.2
The decision to optimize only the initial conditions while keeping all other parameters fixed is understandable for tractability and stability, but could limit representativeness of the extremes. Is this a true limitation for your study? If so, I suggest mentioning it explicitly.

The mention of 1.4° resolution in this section is confusing. It is not clear how or when this configuration is used. The text should clearly distinguish which experiments are at 2.8° and which at 1.4°, and why both are mentioned at this stage.

The discussion of grid scales, time steps, and numbers of simulations is unclear. Are multiple optimized runs performed, or only one? Is the 75-member ensemble used for both the stochastic NeuralGCM and the optimized runs?

If only one optimized run is presented, how robust are the results to “luck” in initialization? How should the uncertainty in the optimization outcome be quantified?

Table 1 is useful, but please explain what the listed parameters mean (like all the \lambdas), why there are two different numbers of steps, and recall the definition of \tau.

Section 2.3
Please clarify how you treat events separated by only one day: are these counted as two separate events or merged as one? Otherwise there is a risk of double-counting.

This section suggests that heatwave intensity is central to the study, but it seems to be used primarily in Fig. 4e. Consider clarifying that it is one of several diagnostics used.

Section 3.1
On page 7, the reference should be to Fig. 4, not Fig. 2 (caption).

The evaluation against ERA5 is valuable, and I appreciate the authors’ transparency in acknowledging that NeuralGCM underestimates extreme heat. Could you provide a possible explanation here (e.g., omission of land–atmosphere feedbacks, as later discussed in Section 4)? Even a brief cross-reference would help.

The distribution in Fig. 1a appears bimodal for NeuralGCM. Is this an artifact, or is there a physical reason?

In Fig. 1b, please add a legend to indicate lead times, and specify the simulation period in the caption (otherwise “Day of the month” is hard to interpret).

While you compare against ERA5 temperature, can NeuralGCM also reproduce circulation fields relevant to heatwaves (e.g., Z500)? Showing this would be useful.

As far as I understand, Section 3.1 uses the 2.8° version of NeuralGCM (worth recalling at the beginning of the section). Since you later show (Section 3.4) that the 1.4° configuration reduces biases and better captures PN2021, it would be valuable to include an ERA5 comparison for the higher resolution as well. Even a supplemental figure would highlight the importance of resolution for heatwave fidelity.

Section 3.2
The optimized trajectories are compared with the stochastic ensemble, but not directly with ERA5. Could you show whether the optimized Z500 patterns resemble those observed?

How many optimized trajectories were run? Is it 75, like the stochastic ensemble, or fewer? Please clarify in the text.

You report a 33% reduction in computational cost. How was this calculated? Please provide details.

Is there an optimal way to select the number of optimization steps ?

Please ensure consistency in the definition of “intensity” across the manuscript, and cross-reference to the section where it was defined.

Section 3.4
Why is the 1.4° experiment presented more briefly than the 2.8°, even though it shows better agreement with ERA5? Presenting the 1.4° case in more detail (with the 2.8° as a supporting comparison) would seem the more logical choice.

Conclusion
The statement “a fraction of the computational cost” is vague. Please quantify—e.g., what fraction compared to a 75-member ensemble?

Final Remark
Overall, I found this to be a promising and well-motivated study, but one that would benefit from greater clarity in the methodology and results sections. The suggestions above aim to improve accessibility and transparency for readers. I believe the manuscript is suitable for publication after these issues are addressed.

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Citation: https://doi.org/10.5194/egusphere-2025-3748-RC1

Tim Whittaker and Alejandro Di Luca

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Short summary

Heatwaves are becoming more extreme in frequency and intensity. Yet running many climate simulations to find the rare worst-case events is slow and costly. We developed a method that tweaks initial weather conditions to target the most extreme heat scenarios at a fraction of the usual cost. For the 2021 Pacific Northwest heatwave, it found cases up to 3.7 °C hotter than any run in a 75-member ensemble, helping communities prepare for the worst.


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