Bottom&ndash;up approach for mitigating extreme events under limited intervention options: a case study with Lorenz 96

Mitsui, Takahito; Kotsuki, Shunji; Fujiwara, Naoya; Okazaki, Atsushi; Tokuda, Keita

doi:https://doi.org/10.5194/egusphere-2025-987

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https://doi.org/10.5194/egusphere-2025-987

Preprints

21 Mar 2025

| 21 Mar 2025

Bottom–up approach for mitigating extreme events under limited intervention options: a case study with Lorenz 96

Takahito Mitsui, Shunji Kotsuki, Naoya Fujiwara, Atsushi Okazaki, and Keita Tokuda

Abstract. Prediction and mitigation of extreme weather events are important scientific and societal challenges. Recently, Miyoshi and Sun (2022) proposed a control simulation experiment framework that assesses the controllability of chaotic systems under observational uncertainty, and within this framework, Sun et al. (2023) developed a method to prevent extreme events in the Lorenz 96 model. However, since their method is primarily designed to apply control inputs to all grid variables, the success rate decreases to approximately 60 % when applied to a single site, at least in a specific setting. Herein, we propose an approach that mitigates extreme events through local interventions based on multi-scenario ensemble forecasts. The success rate of our method is markedly higher than that of Sun et al.'s method, reaching 94 % even when applying interventions at one site per step, albeit with a moderate increase in the intervention cost. Furthermore, the success rate increases to 99.4 % during interventions at two sites. Unlike control-theoretic approaches adopting a top–down strategy, which determine inputs by optimizing cost functions, our bottom–up approach mitigates extreme events by effectively utilizing limited intervention options.

Received: 02 Mar 2025 – Discussion started: 21 Mar 2025

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Takahito Mitsui, Shunji Kotsuki, Naoya Fujiwara, Atsushi Okazaki, and Keita Tokuda

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-987', Qin Huang, 23 Apr 2025
General Comments:
This manuscript demonstrates successful mitigation of extreme events in the Lorenz 96 (L96) model by applying localized interventions. Building upon the work of Sun et al. (2023) on control simulation experiments using LETKF-based data assimilation, the authors develop a control algorithm that selects intervention sites based on multi-scenario ensemble forecasts. The results show significantly improved success rates in reducing extremes - from approximately 60% in Sun et al. (2023) to 94% for one-site interventions and 99.4% for two-site interventions - with robustness demonstrated through sensitivity analyses of the success-cost trade-off. By focusing on limited and spatially constrained interventions, this work advances the feasibility of controlling chaotic systems under realistic operational constraints. As a radically new area of research in extreme weather control, this study represents a compelling step forward.
Specific Comments:
DA method comparison - This study uses LETKF for data assimilation, following Sun et al. (2023), which makes sense for a high-dimensional system like L96. Several other studies in this area (e.g., Miyoshi & Sun 2022; Kawasaki & Kotsuki 2024; Nagai et al. 2024) use EnKF, particularly with the lower-dimensional L63 model. It could be helpful to briefly clarify the rationale for choosing LETKF here, and short comments on whether the assimilation method affects control outcomes (even qualitatively) could be of interest to readers.

Control method comparison - While the manuscript positions the proposed method as a bottom-up alternative to top-down strategies like MPC, it does not include direct performance comparisons. A brief discussion of how the approach compares relative to recent MPC-based or other CSE studies could help contextualize its contributions. If direct comparisons are not feasible, outlining conceptual trade-offs or implementation differences would help clarify the novelty and practical significance.

Optimal control - The current method selecting intervention scenarios by minimizing the maximum ensemble outcome is effective but not optimal. While other top-down strategies determine inputs using optimization minimizing costs, this utilizes limited intervention criteria.

Perturbation magnitude - In Fig. 4 (one-site) and Fig. 8 (two-site), the reported perturbation magnitudes (642.1 and 674.9, respectively) seem quite large. It would help to clarify the units or scale used, are these relative to system variability, or absolute values in state units? Also, Fig. 4 references "operation energy" - what exactly does this refer to? The average number of changes (22.4, 22.1) are shown as non-integers, since interventions are presumably discrete in time, why are these fractional? Is this an average over ensembles or multiple trials?

Overall, these suggestions are meant as optional additions - the manuscript is already very complete and well-structured. Including a bit more comparative context could further enhance clarity for readers unfamiliar with the broader control and data assimilation literature.
Technical Correction:
No technical correction suggested.
Citation: https://doi.org/10.5194/egusphere-2025-987-RC1
- AC1: 'Reply on RC1', Takahito Mitsui, 15 May 2025
  
  Thank you very much for reviewing our manuscript in detail and providing us with valuable feedback. We have addressed your comments and questions point by point and proposed several changes to the manuscript. We believe these revisions will significantly enhance the quality and clarity of our work.
  To improve the readability of our responses, we have applied type coding to distinguish our replies from your comments. For precise formatting and clarity, we have prepared our responses using LaTeX and attached them as a PDF document.
  
  Citation: https://doi.org/10.5194/egusphere-2025-987-AC1
RC2:
'Comment on egusphere-2025-987', Anonymous Referee #2, 01 May 2025

In this work a new approach is presented for mitigation of extreme events, which is based on multi-scenario ensembles and integrated with an ensemble-based data assimilation system. The approach is evaluated in a perfect toy-model scenario showing good results. The paper contributes to the development of methodologies for extreme-event mitigation. The manuscript is well written, and the figures and discussions are appropriately presented. I do not have main concerns with this paper. There are, however, some mainly minor issues that I believe should be addressed for the improvement of the manuscript.

L115-120 The notation and explanation of the two intervention scenarios presented here are not so clear. In the “intervention-off” scenario, is there any intervention prior to time s? In this scenario I assume u can be nonzero at different grid points. Is that correct?
In the one-site intervention scenario, u is nonzero at one grid point only but can also be nonzero before time s and after time s+6 hr. Is ui(t) constant for t > s + 6 hr? Is the intervention forcing u a constant (e.g., given that the forcing will be applied at grid point i, is the value of this forcing known a priori or is it something that will be optimized)?

Figure 2: What do the second panels of Figure a) i) and ii) mean? Also in Figure b)iii), ALERT instead of ALEAT.

L137 Multi-scenario ensemble forecast and local intervention:

L145 In the sentence starting with “Other criteria … “ I can not clearly follow the difference from the previous criterion.

L152 In this part the approach to evaluate sampling errors in the resulting scores is discussed. Why did the authors decide to work with smaller samples instead of applying bootstrap to the whole sample?

L167 “This metric is particularly relevant …” My impression is the opposite: when the intervention is static, scenarios can not be changed, and this metric is not relevant.

In the discussion of Figure 4, the method of Sun et al. is compared with the new method. In the first comparison the success rate is much higher for the new method. However, this is done for a larger intervention size and for a shorter forecast window than in Sun et al. Figures 5 and 6 show that under similar intervention energy and forecast length, Sun et al.’s method are closer to the results obtained with the proposed method. A similar comparison is presented in the abstract and in the conclusions; however, it is unclear if the numbers commented on in the abstract correspond to the numbers in this section. If so, the claim of the abstract and the conclusions does not seem to be a clear comparison with Sun et al.’s approach.

L190: “... necessary is not guaranteed”. Can this be assessed from the previous experiment? The distribution of the distance of the optimal interventions with respect to the location of the extreme event can be obtained and analyzed to support this claim.

Figure 7. Panel c describes the number of scenario changes. This metric seems to grow rapidly from 1 intervention-eligible site to 3. However, I wonder what the behavior would be if the distance associated with each change is also taken into account. It would make sense to distinguish between many small changes and few larger changes (also considering that sometimes the change needs to be done in a small time frame).

L211 complete instead of complete.

L214 Figure 11?

L215: Why is the ensemble size increased in this experiment? I understand that the localization scale has to be adjusted when the observation network is changed; however, increasing the ensemble size is assumed to always lead to a better performance of the filter (particularly at these relatively small ensemble sizes), but always limited by the available computational power.

Citation: https://doi.org/10.5194/egusphere-2025-987-RC2
- AC2: 'Reply on RC2', Takahito Mitsui, 15 May 2025
  
  Thank you very much for reviewing our manuscript in detail and providing us with valuable feedback. We have addressed your comments and questions point by point and proposed several changes to the manuscript. We believe these revisions will significantly enhance the quality and clarity of our work.
  To improve the readability of our responses, we have applied type coding to distinguish our replies from your comments. For precise formatting and clarity, we have prepared our responses using LaTeX and attached them as a PDF document.
  
  Citation: https://doi.org/10.5194/egusphere-2025-987-AC2

Takahito Mitsui, Shunji Kotsuki, Naoya Fujiwara, Atsushi Okazaki, and Keita Tokuda

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Short summary

Extreme weather poses serious risks, making prevention crucial. Using the Lorenz 96 model as a testbed, we propose a bottom-up approach to mitigate extreme events via local interventions guided by multi-scenario ensemble forecasts. Unlike control-theoretic methods, our approach selects the best control scenario from available options. Achieving up to 99.4 % success, it outperforms previous methods while keeping costs reasonable, offering a practical way to reduce disasters with limited control.


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