This paper proposes a ridge regression approach to the detection and attribution of externally forced changes in mean and extreme precipitation. This is an interesting idea that certainly merits exploration, but before devoting a lot of time to understanding the details of the paper and the results that are obtained, I think it is necessary for the authors to better explain their method and to situate it within the pantheon of methods that are already available for detection and attribution.

Ridge regression is a technique that “regularizes” regression problems, such as that described in equation (1) of the paper, in which the predictor variables contained in matrix X are multi-colinear. In the generalized least squares formulation of the regression used in detection and attribution this matrix is composed of model simulated estimates of the responses to external forcing in the form of space-time patterns of change. Depending on variable, period considered, domain of interest and how data are processed, the expected space-time patterns of responses to different forcing factors (often called fingerprints) can be strongly correlated, which results in a  regression “design matrix” X that may be ill-conditioned. Ridge regression is a technique that can be used to overcome this problem, although I imagine at the cost of introducimg some bias into the estimated signal scaling coefficients β. Note that referring to these coefficients as “fingerprints” seems unusual to me.

The concept of regularization, however, also arises in a second way in the detection and attribution problem. Considering again equation (1), the generalized least squares approach (and also its total least squares extension) requires knowledge of the variance-covariance matrix of the residuals ε, which are regarded as resulting from natural internal climate variability. Thus, the variance-covariance matrix is generally estimated from unforced control simulations, using as many climate-model simulated realisations of ε as possible. Even though many climate-model simulated realizations of ε are now generally available, the estimated variance-covariance matrix may not be of full rank or may remain uncertain. Thus, it is also often regularized, using an approach similar to the regularization used in ridge regression, but applied to the noise term rather than the signal term of equation (1). See Ribes et al (2013a, doi:10.1007/s00382-013-1735-7, and 2013b, doi:10.1007/s00382-013-1736-6). Presumably one would want to regularize both aspects of the problem, and also take signal uncertainty into account as is done in the total least squares approach to the regression problem (see again Ribes et al., 2013a and 2013b, and also Allen and Stott, 2003, doi:10.1007/s00382-003-0313-9).

How the combined model represented by equations (1-3) relates to existing techniques, and now the noise that results from internal variability comes into play and is accounted for in their subsequent application in the paper is not made clear, and I think should be clarified before results can be considered.

Also, I think it is necessary for the authors to discuss whether the proposed methods, which basically use linear statistical models that therefore implicitly assume Gaussian, or near Gaussian errors, are suitable for the data to which they are applied. Indicators of extreme precipitation, such as Rx1day at individual grid boxes, are certainly not Gaussian.

A final general comment is that the relatively heavy of use of acronyms in this paper is not very reader friendly.

Overall comments:

This study conducts a signal detection analysis for global changes in mean and extreme precipitation using three observational datasets and CMIP6 multi-model outputs. The authors apply a ridge regression (RR) method to construct fingerprints, which helps increase a signal-to-noise ratio of precipitation change patterns. Results show a robust detection of anthropogenic signals in all observations for both mean and extreme precipitation even when removing global mean trends, further supporting the human-induced intensification of global hydrological cycle. I find this paper very well written with sufficient details provided about methods as well as various sensitivity tests and therefore suggest publication after addressing some minor issues.

Major comments:

1. Although method details are provided, it would be useful to explain more clearly what are benefits of the attribution approaches employed, including ridge regression, EOF-based metric for target variable, and GMST-based signal estimation. All of these procedures seem to contribute to increase signal-to-noise ratio but how they do and what step is more important. The authors provide some associated results from sensitivity tests but an overall explanation of their method possibly with a schematic would be helpful for readers to understand the contribution of each step to the final signal detection.

2. An important motivation of considering different periods and datasets is opposing conclusions by previous studies about model overestimation or underestimation of the observed trends. I am wondering if the authors can go further and compare their results with some previous studies. For instance, if studies based on the latter half of 20^th century trends find model underestimation, the authors can assess their model trends for the same/similar periods. Another point here is that the present study uses absolute units of precipitation while most of previous studies considered relative changes or aggregated values. It would be good to discuss possible influences of this difference.

3. The lower detectability in GHCNDEX observations are suggested to be due to the poorer spatial coverage. Regarding this issue, I would suggest using Rx5d. As I understand, Rx5d has larger spatial coverage than Rx1d and comparison with Rx1d-based results may provide a way to support the authors’ interpretation. Another way would be to compare detection results from using a selected model run but with different spatial coverages applied.

Minor comments:

L8: Indicating analysis period or trend period with signal detection would be useful here.

L17-19, L58-64: Better comparisons can be made by applying the same periods as those used in previous studies. See my major comment above.

L20-21: Is this confirmed by repeating detection analysis using NH-extratropics only?

L34: “discrepancies with respect to observations”. Its meaning is unclear.

L69-71: Need to explain what the previous studies have found additionally using these “data-science methods”. Also, what’s the novelty of this study compared with them? Is it detection based on spatial pattern information alone?

L108-109: “Trend biases due to this structural difference … negligible”. But the cited reference considered south-east Australia only?

L201: How to define S when global means are removed?

L212: “CMIP6 ssp245” should be “CMIP6 historical”?

L227: “virtually identical”. adding spatial correlation would help with this.

L314-316: This suggests possible dependence of Rx1d FRE on temperature, resembling global warming slowdown due to PDO influence?

L331-332: “results … hold when the global mean is used as FR target”. Then what are benefits of using EOF-based metric for target variable?

L382-383: “accuracy of the CMIP6 climate models in simulating the processes …”. It’s unclear how the authors get this conclusion. Observation-model agreement in residual variability? More explanation would be useful.

L394-395: “(not shown)”. This looks important and I suggest showing them in the supplement.

L428: “value of RR-based fingerprint construction”. What happens in detection or SNR without applying RR? See my major comment above.