This is an excellent presentation of a state of the art compilation of magnetic survey data to produce a comprehensive data grid. The authors provide clear discussion of the approach and rationale for their modeling decisions.

I have made a few comments and suggestions as shown in the attached annotated manuscript.

One recurring comment deals with the use of the term "error" when "uncertainty" is meant. Errors can be positive or negative whereas uncertainty indicates the probable range in which the true value is likely to occur. You can only know error if you know the truth for comparison. 

The authors deal with uncertainty in a general probabilistic way - they mention the initial data uncertainty attributed to the original survey data (ranging from 5 to 50 nT as an average attribute per survey). This value is used for weighting of the data in the inversion for equivalent source values. They mention the overall goodness of fit for the equivalent source combined model relative to the original data. They also explain the method for solving in the inversion for the probable DC offset between the individual surveys. An addition source of uncertainty is the long wavelength uncertainty in the LCS-1 model incorporated in the final grid. I realize it is difficult to propagate uncertainty through all these steps, but I think it is worth some discussion and, ideally, the authors would produce some sort of overall uncertainty grid to accompany the data grid.

Another approach to validating the grid and uncertainty would be to identify trusted long survey lines that were not included in the model for comparison with values extracted from the grid. 

However, even without additional discussion/assessment of grid uncertainty, this paper is excellent and worthy of publication. Similar scale data compilations to date have generally not included detailed uncertainty assessment. Similarly, many authors conflate the terms error and uncertainty and most readers can discern the difference.

The manuscript by Heincke et al.  on compilation of magnetic data for Greenland is a very important contribution and based on sound modelling and processing principles.  I have attached an annotated version with suggestions for modifications (grammar mainly) and some questions/comments the authors should consider.

I would like to see some discussion on the actual "models " that are the output from the inversion, even though that they are not "true physical" geo-models In particular, I note (see comments in annotated manuscript) that only induced polarization is assumed. What kind of equivalent source model is produced offshore where you have reversed polarity of the magnetic anomalies. What kind of pattern on equivalent source strength (positive/negative) is revealed? How does remanent magnetisation influence the inversion?

Best regards

Thorkild