Dear Authors,

Referee#1 rated positively your revised manuscript. Referee#2 did not provide any further comment while a third Referee has just provided the comments reported below. I am therefore inviting you to proceed with a further, major revision of your manuscript following those comments and suggestions.

Best regards.
Stefano Pierini
Handling Editor

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Review of “An Adjoint-Free Algorithm for CNOPs via Sampling” by Bin Shi and Guodong Sun.

General comment.

The manuscript is intending to generate Conditional Nonlinear Optimal perturbation using a sampling approach, based on rigorous mathematical approach. The approach is applied in the context of two models, the Burger’s equation in which analytical results can be deduced, and on a more “meteorologically” oriented model, the Lorenz 96 model. Although I see a lot of potential in this approach, I must say that I cannot really figure out what was done and what is the usefulness of the approach. This should be clarified before being able to recommend publication. The main concerns I have are the following

1. It is said in the abstract that machine learning approaches are used in the current manuscript. I do not see any place where such tools are used, unless I am mistaken. This is misleading for the reader. This should be revisited in the whole manuscript.

2. In Section 3, the method is outlined based on some demonstration of theorems, but there is no information on how the approach is implemented and compared with traditional methods. Please revisit completely this aspect in order to show the way to follow in order to develop the method by others.

3. I have really hard time to read and understand the English. It should considerably be improved to make the results understandable.

As the English is really poor, I do not provide any typographical corrections. The full text should be revisited in details.