Aerosol-cloud interactions (ACI) continuously consist one of the largest uncertainties in climate radiative forcing and projections. This study combines a large ensemble of satellite observations and a statistical relation-regression method to estimate radiative forcing associated with key ACI elements, including Twomey effect, liquid water path (LWP) adjustment and cloud fraction adjustment. They found cloud fraction adjustment could be much more important than commonly believed and larger than Twomey effect in ACI cooling; while, LWP adjustment leads to slightly warming globally. The scope fit well with ACP. The manuscript is well written, the results are scientific interesting and politically meaningful supported by sound methodology. I am happy to recommend for publication after a few minor revisions.

Minor concerns:

1) Authors find the LWP adjustment leads to warming almost everywhere globally (Fig. 2); however, recent studies, which also use a large ensemble of satellite observations, reported that LWP adjustment leads to SW cooling on a large-scale (Manshausen et al., 2022;Rosenfeld et al., 2019). Could you please add some more discussion about this discrepancy?   

2) Page-3 bottom equation. Here, authors describe radiation anomaly as a function of cloud fraction (C), and the partial dependency: dR/dCrl, where C is partitioned by effective radius (r) and LWP (l). I wonder that are ‘r’ and ‘l’ the most important controlling-factors for C, or is there also other factors would largely impact ‘C’ and the partial dependency relationship (dR/dC)?

3) Some more clarification about the method would help audience better understand it. A) line-100 (and after), what does ‘anomaly’ here refer to, do you mean anomaly to the climatological value (temporal averaged, or also spatial averaged)? B) line-120: some description about how do you remove the climatological seasonal cycle and linear trend. C) line-125: explain 46-49% variance – how do you measure variance and lead to this conclusion?

4) Fig. 1. Joint histogram. I do not quite understand this figure. Does the color indicate the values of cloud fraction (a) and SW kernel (b)? If yes, then this is not a joint histogram, it is a heatmap plot. A histogram should show the probability density function (or counts) of data.

Moreover, Fig. 1b. the kernel dR/dC should be depended on latitude/longitude/day-of-the-year/surface-albedo. Does all of these factors are controlled, e.g., fixed to an average value, and only allow re and LWP to vary?

5) Data open-access. SW kernel data is a key factor use in this study and generated in this study. I feel that making the global distribution of this dataset open-access would largely improve the reproducibility of this study, and also enhance its contribution to the community.  

References:

Manshausen, P., Watson-Parris, D., Christensen, M. W., Jalkanen, J.-P., and Stier, P.: Invisible ship tracks show large cloud sensitivity to aerosol, Nature, 610, 101-106, 10.1038/s41586-022-05122-0, 2022.

Rosenfeld, D., Zhu, Y., Wang, M., Zheng, Y., Goren, T., and Yu, S.: Aerosol-driven droplet concentrations dominate coverage and water of oceanic low-level clouds, Science, 363, eaav0566, 10.1126/science.aav0566, 2019.

Please see the supplement for comments.