The idea of the paper is to combine various data records on snow water equivalent (SWE) with ridge regression model (RRM)  technique. This is an interesting and welcomed approach that possibly provides improved estinates on SWE of the northern hemisphere. However there are some issues that need further consideration and clarification.

Apperently, the paper applies point-wise observations on snow cover, not distributed observations from snow courses. Thus the reference data doest not directly describe the SWE on the scale of data products. Moreover, the NOAA GHCN data does not include direct measurements on SWE (they are evidently based on snow depth observations at meteorological stations). Thus, the applied reference data may include systematic errors due to inadeqate consideration of temporally and spatially varying snow bulk density.

The authors should also note a limitation that reanalysis data-based products (that are used here together with obsrvational data-based products) on SWE do not provide model-independent data (results here are not independent on models).

 Detailed comments:

Title: Since the study region includes all land areas north of the latitude of 45 degrees, the term Pan-Arctic is not good.

Lines 59-61 and 96-98: The authors should note that a recent investigation (Pulliainen et al. 2020) applied a bias correction to GlobSnow and reanalysis data products to obtain improved estimates on peak annual regional and hemispehric snow mass/SWE. This was done using hemispheric snow course obervations.

Lines 139-166: The method should be explained in more detail. In Eq. (1) p probably includes as variables the applied five SWE products, but how is the DEM considered? What is the number of samples N in the training data set? How is the training and testing data set defined/selected?

Lines 278-279 and 306-308: How is the annual average SWE calculatated, mean value across the whole year?

Lines 467-468 (Fig. 1): Some data stations (RSSD) are located in the open Norwegian Sea, and transect of stations in Canada is odd. Are these observations from some campaign?

Lines 508-510: The wide spread of range is y-axis is odd.

References:

Pulliainen, J,, Luojus, K., Derksen, C., et al. Patterns and trends of Northern Hemisphere snow mass from 1980 to 2018, Nature, 581: 294-298, 2020. 

A very interesting paper to develop an improved SWE dataset based on existing multi-source SWE products using machine learning. However, there are some points which need to be well addressed. Please see following comments:

1. The ridge regression machine learning algorithm in Section 2.3 needs to be better described.

• Why ridge regression is selected among so many machine learning algorithms? The advantages of using ridge regression over others for this application need to be highlighted.
• What is the requirement of ridge regression in terms of variable dependence? Does it require predictor variables and target variable independent? Are the station data from GHCN or Russian snow survey used (or partially used) for generating the gridded SWE products used in this paper? If so, the target variable and predictor variables are intrinsically related. How does this impact this algorithm? Please provide more information to explain and justify.
• It is unclear how DEM is used in the ridge regression. Is it used as a predictor variable in addition to AMSR-E/AMSR2, ERA-Interim, GLDAS, GlobSnow, ERA5-land SWE or just used to evaluate different model performances related to elevation? There are many important factors impacting the SWE estimation in addition to DEM. Have you also considered adding more variables to further improve the model? Please provide more information to explain.
• The authors mentioned in the model training process, ‘‘... reduced the training data appropriately for the regions with denser training data, and make it close to the amount of training data in the sparse region’’ Please be more specific how this is done. Is it through randomly selecting training data in the regions with denser data? If so, what is the amount of the training samples used? Please provide more information.

2. What is the range of the generated SWE product? Would be nice to see the range of generated SWE, and also the performances of SWE at different ranges. In Figure 4, it shows the data all below 400mm. What is the capability of this RRM product for capturing deeper snow? Please add more descriptions or discussions on this.

3. In Figure 1, the stations block the DEM information, making it difficult for the audiences. I would suggest to change figure 1 into a two-panel figure, with one for stations and the other for DEM.

4. From Table 2, the improvement of RRM product is not so big as compared to ERA5-land and GlobSnow SWE alone. It would also be nice to see the comparisons with other fusion methods, such as the simple multi-source data average or regular linear regression. Also, it shows that GLDAS SWE has poor performance as compared to other products. Have you considered to leave it out and further improve the machine learning model?