Overview

In this paper, ridge regression is used to systematically evaluate the addition of five candidate cloud controlling factors (CCFs) to previously established core CCFs within large spatial domains to predict longwave high-cloud radiative anomalies. The results show that upper-tropospheric static stability is an important CCF for high clouds and longwave cloud feedback. All combinations of tested CCFs perform quite well for most locations at grid-cell scales, while differences between configurations for predicting globally-aggregated radiative anomalies are more pronounced. The authors found that spatial domain size is more important than the selection of CCFs for predicting local anomalies, and there is discrepancy between optimal domain sizes for local and globally-aggregated radiative anomalies.

There are abundant technique details in the paper, and the method is potentially useful to evaluate the long-term high-cloud feedback. The paper might be accepted after addressing the following comments:

Specific comments:

1. In machine learning, the dataset used to test the performance of a machine-learning model should be independent from the dataset that is used to train the data. What is the training dataset and testing dataset for the metrics of Fig. 2? Ideally, the PI-control or AMIP simulations might be used as the training dataset, and abrupt4xco2 simulations might be used as the testing dataset. For observations or historical simulations, the first several or more years might be used to train the ridge regression model, and the last several years might be used to test the performance of the model.
2. R-square and r are highly relevant metrics, so I suggest using only one of them in the main text.
3. The none-local effect of CCF on high cloud amount might be further explored and discussed. The dependence of model performance to domain size might be associated with cloud transferring between adjacent grid boxes. In addition, previous studies suggest that the surface temperature in the tropics has significant impact on subtropical high cloud amount, is this process associated with the domain size dependence?

Minor Comments:

It is recommended to check all instances of italicized text in the manuscript to ensure consistency throughout the text:

Line 99: delete the preposition “in”.

Line 275: what is the variable “r”?

Line 287: where the second term on the right-hand side of Eq. (3) ...

Figure 1: The latitude and longitude coordinates should be marked on the map (and similarly for the subsequent figures).

Table 1: The formatting needs to be unified. For example, there are excessive gaps between certain words, and the sixth row of the table ("Key studies") lacks a space before it. Moreover, the last row ("Key studies") has a period, while the other rows do not.

Figure 4. The colormap of this figure looks not as good as other figures. I suggest using same colors as Fig. 3.

Figure 9: I suggest adding an additional panel to compare the results with the CN21 method (i.e., CCFs containing only T_sfc, RH_700, UTRH, and ω_300). This comparison will better highlight the advantages of the new method.

General comments:

In this manuscript, the authors use ridge regression to extend the work of CN21 to analyse LW cloud radiative anomalies in the form of Cloud Controlling Factor (CCF), i.e. relationships between large-scale satellite cloud observations and meteorological predictors. Logically, they focus on high clouds. They define a set of four “core CCFs” and of about ten “candidate CCFs”. The authors present the method, variables and data in the first four sections, followed by the results in the fifth. I'm not expert enough in their ridge regression method to give a relevant opinion on the statistical validity of their work, and I consider it relevant.

The skills metrics for the various indicators are examined in sections 5.1 and 5.2, in particular on the basis of Figures 2 and 5. I find this part of the manuscript particularly problematic. The most systematic and robust variation of these CCFs is as a function of the size of the domains considered, and this aspect is little discussed. Most of the discussion focuses on the variation of the metrics according to the CCF. But, for the same size of domain, these variations are extremely small, of the order of 1% for the RMSE of local predictions, of 10% for the Pearson number of the integrated value of predictions, i.e. often of the order of the last digit given. There is no discussion as to whether this level of precision is relevant. Some variations may be different depending on the size of the domain. There is a lot of discussion about how these indicators evolve according to the CCFs, but this evolution between CCFs is difficult to see. Given that it is mainly the dependence on CCFs that is being discussed, why not plot the values for a single domain dimension (as in Figure 6)?

These variations in performance according to the CCFs are generally very small, which leads the authors to make many suppositions but few assertions. The word "speculate" appears 15 times in the manuscript. Moreover, these small variations in performance according to the CCFs make many comments questionable in my opinion.

I have the same criticism of figure 7 and the associated comments. The observations are very noisy, as you would expect, which makes it difficult to compare the figures directly. It would therefore be necessary to highlight what is significant and what is not, to show zonal averages, smoother results, and so on.

In summary, this manuscript deals with an important subject and uses an original method of analysis, but needs major revisions in order to make the text less descriptive, reach more conclusions and ensure that these are better supported.