Overall, I find this submission to be a relevant contribution to the climate science community as it provides a comprehensive overview of ongoing research, outlines current road-blocks and specifically suggests promising approaches which were previously over-looked or unknown in the field. Therefore, I highly suggest to improve upon the clarity and structure of the abstract, introduction and conclusion. This is necessary, as I find the importance of this contribution sometimes gets lost in overly long and disjunct paragraphs and sentences. While, I like the designated re-iteration of the potential application examples in the conclusions, I suggest to improve these by focussing on the discussed ways of using equation discovery in each application.  My detailed review can be found in the supplement.

Review ESD

Overall:

The topic of the paper is timely and highly interesting, and the ideas presented in the paper are definitely worth publishing. The introduction part and the method part are well written and give a good overview. The main issue I see with the paper in its current form is that while the intention of the paper is obviously to provide ideas for AI solutions, most of the example part (part 3) of the paper discusses existing solutions or problem settings, without reference to potentially new solutions. For example, all three figures that describe the examples do not make any reference to any proposed new solutions.

Having said that, the ideas are definitely there in the paper, but especially in part 3, they tend to drown in overly long discussions of the domains of the examples, instead on focusing on potential use of AI.

Therefore, while there is nothing fundamentally wrong or flawed with the paper in its current form, I would strongly encourage the authors to restructure especially part 3. Some ideas:

• Make the text focus more on potential AI solutions
• Replace the existing figures – which have a lot of details on the domains – with conceptual figures. With this, readers would be at a single glance be able to spot your ideas

Other comments

it might be worthy to briefly mention explainable AI as well, and what differentiates equation discovery from it.

p.5 maybe mention weather clustering, which is widely used

part 3.1: it is a bit unclear to what the task of an AI part would be in detail. There is in my opinion too much detail of the physics around it, and too little detail on how to solve the problems using equation discovery. E.g., instead of fig.2, which shows a lot of details on a convective storm (something that is actually not the topic of this paper), I think it would be more beneficial to have a conceptual graphic showing how to use equation discovery in this context.

3.2: same as for the first example: a conceptual figure on what is actually attempted would be very valuable.

p.15 L5-6: ” ML-derived spatial aggregation is a form of technique known as computer vision”. Computer vision is a very broad field, so this sentence is incorrect. I also do not understand what you exactly mean here with “ML-derived”.  Again, less focus on the state of the field (here carbon cycle modeling) and more focus on the actual AI ideas would be better.

3.3 in this section, even more than in 3.1 and 3.2, there is too much focus on existing methods and models, and the ideas using AI get lost in it. For example, I do not see the need of the detailed discussion, including equations, of the simple ENSO model.

p.15 L 22-23 “However, the large computational time of such simulations maintains interest in faster summary models, mainly in the form of coupled Ordinary Differential Equations (ODEs).” This should be reformulated, as it is a bit confusing, since also the high resolution ESMs are based on coupled ODEs.

p.22 L3: the word “threat” seems an odd choice here.

In the paper, it is mentioned a couple of times (e.g. p21 L26) that it is unclear whether AI-developed models, because of their statistical nature, can extrapolate beyond current forcings. In our paper on Lorenz models, we showed – albeit in a highly simplified setting – that AI models indeed can to some extent learn the influence of external forcing and extrapolate it (https://npg.copernicus.org/articles/26/381/2019/npg-26-381-2019.html). This does of course not necessarily generalize to more complex models, but it might be worth mentioning.

General style:

Abbreviations: this is clearly a matter of personal taste, but considering the interdisciplinary nature of this paper, I would suggest to reduce the use of abbreviations. For example, TP (Tipping Points) is an abbreviation that many readers might not be familiar with, and it is anyway used used only a couple of times. Therefore, it would make the paper easier to read if it simply spelled out every single time (when I encountered it in the conclusion section, it took me some time to remember it meant tipping point even though it was mentioned in the introduction).