This emulator, a new addition to the MESMER family, produces fields of monthly precipitation as a function of corresponding fields of monthly average surface temperature. It does so by modeling precipitation at each grid point as the product of a mean component, driven by temperature in a neighborhood of the location, and a residual component whose variability is estimated as constant along the length of the simulation.

The results, for both the case when temperature is the output of the ESM being emulated, and the case when it is in turn a product of emulation by the mean component of MESMER-M, are validated according to numerous metrics that address first and higher order behavior, trends, spatial and temporal coherence within the precipitation output and between precipitation and temperature, with satisfactory results. 

I enjoyed reading this paper, which is clearly written and presents a wide range of validation results creatively conceived and displayed. The authors have a clear-eyed take on the  outcomes, which are not perfect but constitute an important step forward in emulating impact relevant variables. This is especially true for an emulator that can generate novel realizations, akin to additional initial condition ensemble members, and therefore can help characterize statistics of extremes (within the limits of what ESMs and their emulator can represent, through monthly average quantities). As the authors recognize, there is room for improvement, especially for the highest quantiles of precipitation which often appear overestimated when the validation is done within the confines of an individual model statistics, but these errors pale compared to the inter-model variability/differences. It is also good that the authors are able to offer an hypothesis about the sources of the emulator shortcomings (having to do with the variability term being modeled as stationary rather than allowing it to vary with temperature changes as well) and therefore can point at directions for further development.

My comments are in the spirit of creating a slightly more comprehensive picture of the emulator-ESM comparisons (again recognizing the nice effort in providing a multidimensional depiction of the emulator performance, always hard to do). What I would have liked to see are:

• Maps of gridded trends and patterns of change for a few time slices along the century, comparing emulated and ESM projections, maybe as seasonal averages. These could give an additional sense of the mean/trend performance at the grid-point level, performance evaluation which is currently - for these aspects --  limited to aggregated regional (SREX) scales.
• Additional analyses of spatial and temporal characteristics of the generated precipitation fields. These  could be performed for a set of locations, chosen to represent different latitudes/climate conditions. These analyses could include variograms, which are the tool of choice for analyzing  the spatial correlation characteristics of a field from spatial statistics, and could be computed for the regions around each locations. Similarly, for time series of output at specific locations one could look at the entire autocorrelation structure, or spectrum, and have a full picture of what the emulator does well or misses (for example, ENSO-driven oscillations in precipitation at points known to have strong teleconnection, and of course compared to what the ESM does, since it is not a given that ESMs represent those signals well. Hopefully at least one of these three ESMs has a decent ENSO behavior and it would be interesting to see if the emulator can represent it).

My other overarching feedback is that some of the figures are very small and it is hard to distinguish the different points/color hues. Either expanding the area of the page dedicated to them, or reducing the range of some of the axis to focus on the region of the plot where something is happening could help (even if I realize that the same ranges may be needed for ease of comparison). But all this said, I appreciate the graphics that the authors have created to  display these results.

I am aware of another emulator proposed recently, for daily precipitation, that may be relevant as a citation (if only for its use of a Gamma distribution): Kemsley, S. W., Osborn, T. J., Dorling, S. R., & Wallace, C. (2024). Pattern scaling the parameters of a Markov-chain gamma-distribution daily precipitation generator, International journal of climatology, 44(1), 144–159. https://doi.org/10.1002/joc.8320

These are my only substantial comments, and I would be pleased to see a slightly revised version addressing them, but I consider this work in very good shape already so I would characterize my requests as minor revisions and I hope the authors can meet them with ease. Nice work. 

Please refer to the attached pdf for the comments.