The application of control theory, including optimal control theory, to solving problems of weather modification and climate engineering is not new, but at the same time, this problem remains underdeveloped. The application of control theory in meteorological and climate applications has two important aspects.

The first aspect, let's call it physical, is related to the fact that atmospheric processes possess enormous energy, while human technological energy capabilities are orders of magnitude smaller. Therefore, the identification of physically justified methods of affecting weather and climate is a topical issue. For example, this problem can be solved using the sensitivity theory of dynamical systems [1-3].

The second aspect concerns the mathematical theory of weather and climate control. Here too, rather complex problems arise related to the observability and controllability of dynamical systems, which the climate system and its components, including the atmosphere, are. An important and rather complex issue is also the problem of goal-setting, i.e., justification of objective functions (also known as cost functions ot performance indices).

Unfortunately, the key problems of weather and climate control listed above are not even identified by the authors of the reviewed article. I see the reason for this in that the authors seem to be little familiar with a number of works in which the problem of weather and climate control was considered with varying degrees of detail. The list of some articles includes [4-11].

As a model of the atmospheric system, the authors use the well-known E. Lorenz system, which under certain conditions exhibits chaotic behavior. However, it should be kept in mind that the sensitivity and controllability of chaotic dynamical systems have their distinctive features [12,13]. The Lorenz system, in its classical version, as well as in the coupled (fast-slow) version to mimic the atmosphere-ocean system [14,15], is widely used in many fields, including meteorology. This system is mainly used to study the phenomenon of deterministic chaos, as well as to test various new numerical algorithms including AI. However to study the possibilities of controlling meteorological and climatic processes, models must be much more realistic (see for example [7,9]).

The authors essentially solved the problem of studying the sensitivity of the Lorenz system to small controlled perturbations. Meanwhile they did not indicate the problems that may arise in this case [12,13]. The authors also did not at all illuminate the current state of the problem and the current achievements of other researchers, referring only to the work of Miyoshi and Sun. Despite the fact that the work is well written and structured, the authors need to substantially revise it taking into account the above mentioned comments.

References

1. Hall M.C.G., Cacuci D.G. Sensitivity analysis of a radiative-convective model by the adjoint method. J. Atmos. Sci. 1982, 39, 2038-2050.
2. Lea D., Allen M., Haine T. Sensitivity analysis of the climate of a chaotic system. Tellus, 2000, 52A, 523–532.
3. Soldatenko S., Yusupov R. The determination of feasible control variables for geoengineering and weather modification based on the theory of sensitivity in dynamical systems. Journal of Control Science in Engineering, 2016, 2016, 1547462
4. Hoffman, R.N. Controlling the global weather. Bull. Am. Meteorol. Soc. 2002, 83, 241–248.
5. Jarvis, A.J., Young, P.C., Leedal, D.T., Chotai, A. A robust sequential CO2 emissions strategy based on optimal control of atmospheric CO2 concentrations. Climatic Change, 2008, 86, 357 373.
6. Jarvis, A.J., Leedal, D.T., Taylor, C.J., Young, P.C. Stabilizing global mean surface temperature: a feedback control perspective. Environmental Modelling Software, 2009, 24, 665-674.
7. Ban-Weiss, G.A., Caldeira, K. Geoengineering as an optimization problem. Environ. Res. Lett. 2010, 5, 034009.
8. Weller, S.R.; Schultz, B.P. Geoengineering via solar radiation management as a feedback control problem: Controller design for disturbance rejection. In Proceedings of the 4th Australian Control Conference (AUCC), Canberra, Australia, 17–18 November 2014.
9. Soldatenko S.A. Estimating the impact of artificially injected stratospheric aerosols on the global mean surface temperature in the 21th century. Climate, 2018, 6, 85. doi:10.3390/cli6040085
10. Sierra C.A., Metzler H., Müller M., Kaiser E. Closed-loop and congestion control of the global carbon-climate system. Climatic Change, 2021, 165, 15.
11. Soldatenko, S. and Yusupov, R. An Optimal Control Perspective on Weather and Climate Modification. Mathematics, 2021, 9, 305.
12. Wang Q. Forward and adjoint sensitivity computation for chaotic dynamical systems. Journal of Computational Physics, 2013, 235, 1–13.
13. Soldatenko S.A., Chichkine D. Climate model sensitivity with respect to parameters and external forcing. In: Topics in Climate Modeling. T. Hromadka and P. Rao (eds.), InTech, Rijeka, Croatia, 2016, p. 105-135.
14. Pena M., Kalnay. E. Separating fast and slow modes in coupled chaotic systems, Nonlinear Processes in Geophysics, 2014, 11, 319–327.
15. Siqueira L., Kirtman B. Predictability of a low-order interactive ensemble. Nonlinear Processes in Geophysics, 2012, 19, 273–282.

Review of "Evaluation of Effectiveness of Intervention Strategy in Control Simulation Experiment through Comparison with Model Predictive Control"

This article aims to benchmark the Control Simulation Experiment (CSE) framework for controlling chaotic systems proposed by Miyoshi and Sun (2022) with respect to a well-known method of control theory known as Model Predictive Control (MPC). The study uses the Lorenz 63 (L63) model to perform this analysis, with the wings of the butterfly-like attractor defined as "weather regime". The studied control algorithms must prevent the switch from one wing to the other within an Observing Systems Simulation Experiment (OSSE) framework.

General comment

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First, the paper lies on the conceptual side of the field and cites correctly the related literature, which would have been sufficient for an article on the control of chaotic systems alone. However, here the authors introduction shows that they have weather regimes shift in mind and frame it as a step "[guiding] future research efforts aimed at mitigating the impact of extreme weather events through controllability" while not providing any context or link to the literature of such events controllability. For example, the problem of defining what a weather regime is, is in itself an open problem, and some people might find it difficult to equate weather regimes to the wings of the L63 attractor.

But this first point could be easily addressed by rewriting (substantially) the introduction and conclusion of the paper.

However, more important problems might lie in the conception of the benchmark itself.

The methodology of the benchmark must be detailed more thoroughly and this is why I will suggest a major revision, with a subsequent revision (from me, but also ideally from other reviewers).

I will now detail this:

CSE methodology

-------------------------------

The problems start with the description of the CSE framework. In Miyoshi and Sun, they (rightfully) take a great deal of precaution stating that "It is essential that our prediction and control system is blind to the NR and takes only the imperfect observations." .

The NR is the nature run, and within the OSSE framework, it is a synthetic independent run of the model which is supposed to represent the "truth" (for example the true atmospheric state). However, the authors here never mention the existence of this crucial run in Section 2. When CSE impacts the NR (by perturbing the true atmosphere), it is supposed to represent an actual action on reality, yet the authors state in the introduction (line 24) that "By applying infinitesimal perturbations to the atmospheric state

within numerical models, CSE aims to influence the future evolution of chaotic systems toward more desirable trajectories." which hints at a confusion of the authors between a pure model world and a realistic framework containing a natural state to which the perturbations must be applied.

The CSE algorithms presentation detailed in section 2 is not wrong in itself, but hides how the observations are generated.

The point 4.(d) simply states that perturbations should be added to the "Lorenz 63 model at each time step [between two subsequent analysis]”, while actually in real condition, perturbations would be done on the real atmosphere (represented here by the NR).

This is not a problematic description, just an incomplete one of the CSE algorithm. But I think it might lead later to an incorrect comparison with the MPC.

MPC methodology

-------------------------------

MPC applies continuously (i.e. at any time step) perturbations over the whole prediction horizon T. These perturbations are obtained by optimizing (e.g. by gradient descent) the discrete-time forecast model evolution considered as a feed-forward network.

One could question the interest or feasibility to apply constantly changes to the atmosphere, whether or not an extreme event is forecasted.

But that being put aside, it is not clear from the manuscript how the DA is done for the MPC, or if there is a DA process actually involved. In section 3.3, it is said that at each time step the current state of the system is "observed or estimated". Which system ? And what does "observed or estimated" here mean ? In the CSE framework, it was clear that observations were obtained by sampling and perturbing the NR, but here it is not clear what is used as observations. It looks also like the observations take place at every time step, which is unrealistic for atmospheric forecasting systems.

Section 4.2 indicates that the authors tested the 40 initial conditions (IC) provided by Miyoshi and Sun. For instance, in Miyoshi and Sun, the 40 IC are used to generate independent runs of 8000 timeunits with 1000 DA cycles each (i.e. DA takes place each T_a = 8 timeunits). Do the runs used for the MPC have the same total length? Or the same at least the same number of observation/assimilation cycles? This is important to see if both statistics are comparable.

But the nature of the experiments seems also to be different from the CSE ones.

Indeed, it is difficult to know from the manuscript on what these MPC perturbations are applied ? On a NR ? But how was this NR defined?

On the other hand, if there is no NR, then this means that the MPC experiments are not OSSE ones. The authors are then just trying to control runs of a chaotic system (here to the L63, but it could have been any other), forcing its trajectory to satisfy some bounds during a given period. These experiments cannot be linked to any real world system then.

Because of all of this, both experiments might not be comparable.

Therefore, the authors should detail thoroughly the MPC experiment with regards to the points raised above.

Until then, it is not clear if the present study is acceptable for publication.

How to improve the manuscript

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• As said above, the MPC experiments must be better described, in particular how the observations are obtained. This is a crucial point.
• The MPC with temporal deep unfolding must be better introduced in general, with schematics, so that the reader can understand what it is about, what architecture it is. Citing Kishida and Ogura 2022 is not enough and the readers of the geophysics community deserve a proper introduction to this.
• Also the MPCIL is mentioned first in section 4.2, without any prior explanation, so that readers not reading Kishida and Ogura cannot understand what this is. MPCIL must be properly introduced beforehand.

Final words

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Also the code of the study must be shared openly, as it is strongly recommended in NPG.

It should be noted that not releasing the code for studies using the simple L63 model defeats the point of using L63, i.e. providing a conceptual framework where reproducing experiments is easy.