In the manuscript “ML-AMPSIT: Machine Learning-based Automated Multi-method Parameter Sensitivity and Importance analysis Tool” the authors present a software tool to estimate importance of parameters in weather prediction models. The tool is based on the use of several machine learning (ML) models as computationally cheap surrogate models, which can be used to emulate large numbers of experiments and to estimate the importance or sensitivity of the potentially many parameters to be calibrated. The ML-AMPSIT provides the user with several functions that can be used to assess the convergence and the quality of the trained methods, and the multi-method approach also provides an estimate of how reliable the estimated importance is. The authors also present an application of their framework on the Weather Research and Forecasting (WRF) model coupled with the Noah-MP land surface model, by simulating a sea breeze circulation over an idealized flat domain and predicting the effects of 6 parameters on the model output.

Overall, the manuscript is clearly written and understandable. The authors recognize the crucial importance and the challenges posed by sensitivity analysis experiments in the calibration of weather prediction models, which gives the manuscript a clear motivation. The working of the ML-AMPSIT framework is presented well, and so are the results of its application on the case study.

There are only some points where the authors should clarify their statements or expressions, or provide more extensive explanations, in order to improve the clarity and the overall quality of the manuscript. I will list these points below. Once these points have been successfully addressed, I would be happy to recommend the manuscript for publication.

1. In the introduction it is mentioned that “ML techniques have gained traction in weather and climate modeling and observations […] particularly in parameter optimization tasks like calibration”, but I feel several relevant works exploring the use of emulators for tuning weather prediction and climate models, closely related to the long-term aims of the authors as far as I can interpret, are missing. I feel these should be cited. Here are a few examples.
   1. Daniel Williamson, Michael Goldstein, Lesley Allison, Adam Blaker, Peter Challenor, Laura Jackson, and Kuniko Yamazaki, “History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble” (2013)
   2. Fleur Couvreux et al., “Process-Based Climate Model Development Harnessing Machine Learning: I. A Calibration Tool for Parameterization Improvement” (2020)
   3. Katherine Dagon, Benjamin M. Sanderson, Rosie A. Fisher, and David M. Lawrence, “A machine learning approach to emulation and biophysical parameter estimation with the Community Land Model, version 5” (2020)
   4. Duncan Watson-Parris, Andrew Williams, Lucia Deaconu, and Philip Stier, “Model calibration using ESEm v1.1.0 – an open, scalable Earth system emulator” (2021)
   5. Davide Cinquegrana, Alessandra Lucia Zollo, Myriam Montesarchio, and Edoardo Bucchignani, “A Metamodel-Based Optimization of Physical Parameters of High Resolution NWP ICON-LAM over Southern Italy” (2023)
2. In Page 4 it is stated that “There is no upper limit for the number of parameters that can be analyzed”, but of course the higher the dimensionality the harder the training of a surrogate can become, It would be useful to specify here how the number of simulations required scales with the number of parameters.
3. In Page 7, Eq. (2), a definition of the terms V_{i,j,...} is missing, and should be added.
4. In the Sections from 2.3.1 to 2.3.5 it is unclear how these different algorithms are used to compute an importance metric for the parameters. As far as I understood, the Sobol indices (the first-order one specifically) are computed only using Gaussian processes and Bayesian ridge regression. What is then precisely done when using the other ML algorithms explained? This explanation should be added to the manuscript.
5. In Page 10, Section 2.3.6, the authors state that “GPR is a non-parametric method, i.e., it does not make assumptions about the functional form of the relationship between the input and output variables”. The underlying assumptions on the functional form are contained in the chosen kernel, so there are in fact assumptions one has to make when using Gaussian processes. Maybe the authors here mean that there is no assumption of linearity with the chosen RBF kernel (as they specify later on)? Also, it seems that the authors do train the parameters of the kernel (e.g., lengthscale), so the adjective “non-parametric” may be confusing here.
6. In Page 10, Section 2.3.7, it should be specified what E and H in the equations mean in the context of the problem considered.
7. In page 11, Section 2.3.7, the authors state “The same procedure used for the GPR algorithm to leverage the probabilistic output for deriving feature importance coefficients is also implemented here to compute the Sobol first-order sensitivity index”. I find confusing why the probabilistic nature of GPR or BRR is important for the calculation of the Sobol indices. In principle also ‘deterministic’ emulators like neural networks can be used to calculate Sobol indices. Can the authors comment on what they mean with this?
8. In Page 13, the authors write “The spread of the ensemble tends to be larger over water than over land, especially before sunrise, indicating that the variation of the input parameters has a larger effect on v over water”. Since most of the parameters varied were land-related parameters, I find this seemingly counterintuitive. Do the authors have a qualitative explanation for that?
9. From Page 14, when presenting the results the authors refer to the “importance” of the parameters, but no formula for this was given, especially in the context of LASSO, SVM, CART, RF, XGBoost. Please add a proper definition of it in the manuscript.
10. In the end, Page 26, the authors state “It is then clear that ML-AMPSIT significantly reduces the number of simulations needed for sensitivity analysis and extraction of feature importance”. I find this a bit of a strong statement that should be mitigated. It is by no means clear that 20 or 30 simulations will be sufficient to train the emulators to reach faithful outputs. Specifically, as pointed out by the authors, the comparable performance of the investigated methods suggests the absence of strong non-linearities, which obviously renders the training of the methods more efficient. I expect that in presence of strong non-linearities the amount of training data will need to be increased, and so it remains a question as to whether this number will be systematically smaller than the other existing methods.

General comments:  I found the paper by Di Santo et al. to be an interesting contribution to the scientific literature. 

The manuscript presents a framework that  aims at providing a flexible and easy-to-use framework for performing sensitivity and importance analysis for complex models using surogate models generated through several ML techniques.

However, I have identified several areas where improvements could be made. I hope that the authors, reviewers and editor will find the suggestions below constructive and useful.

A general suggestion to the manuscript readability due to the high number of acronyms and codes declared in the  manuscript, is to add an acronym table that condensate abbreviations and, other table in the methodology section with the main characteristics of the mathematical techniques to help the reader to not to be overwhelmed with the immediate information of all these methods and their details

Ending the Introduction to make smooth transitions a connector paragraph is needed to have smooth transitions between sections.

Could be helpful as well an introductory paragraph of the Methods section.

Specific comments:

-In Page 7, Eq. (2). Terms definition missing V_{i,j,...}

-Page 12 Eq(5). Introduce terms in the equation that are not described in the text θ_s and put units into []. What is TOPMODEL?

Paragraph 355, page 13. give more arguments about the selection of the two locations (one over land and one over water), I know are very different locations but explain the reader that you want to have two places that represent different dynamics in the model due to the input parametrizations of each site. 

Section 3.2 Model setup should have a Figure with the characteristics of the domain or at least a table that summarize the main characteristics of the model domains.

Agree with the minor comment on CC1: 'Comment on gmd-2024-56', Benjamin Püschel, 21 Jun 2024 :

"

• The quality of most figures is not entirely satisfying but could be improved with relatively little effort. For instance:
• Add a grid to the background of all figures.
• Increase font size in legends of Figs 3 & 4.
• Increase font size of labels in Fig 5 and title of subplot c).
• Add a second y-axis for the p-value in Figs 5, 8, 9 as it is close to 0.
• Swap x- and y-axis in Figs 12, 13, 14, 15 since height coordinates are usually represented on the y-axis.
• Increase line width and use both colors and line styles to differentiate between lines in all plots. This would greatly increase visibility, especially for color-blind people.
• Is there a reason why the area under the curves is colored in the feature importance timeseries? (Figs 5, 10, 11).

"

About the references section

• Is suggested to add a couple references more from year 2024 to update the state of the art of the manuscript
• Put all the dates in the reference section homogeneously, i.e  all "....(year).....no: "..........(month year)..........."